Best AI for Differential Equations: Top 5 Tools Reviewed
Solving differential equations used to stress me out. If you’re in calc or engineering, you know the pain: hours wrestling with first-order ODEs, Laplace transforms, or those monster PDEs from physics class. I spent a semester trying out every AI math tool I could find-typing in real problems from my homework, scanning my scribbled notes, and paying for the “Pro” versions to see if they’re actually worth it.
Here’s what I learned: AI can save you huge amounts of time, but not every tool is right for every student. Some explain every step. Some just spit out the answer. And prices? All over the place.
In this review, I’ll break down the top 5 AIs for differential equations, show actual examples, and help you pick the best one for your needs (and your wallet).
Key Takeaways
- AI tools can simplify and explain complex differential equations step-by-step.
- Mathpix, WolframAlpha, and Symbolab are my top picks for accuracy and student-friendly features.
- Not all tools are great at both solving AND explaining DEs-choose based on what you need.
- Prices range from free to $7.99/month for full features.
- Always try the free versions first with your real homework to see if they fit your class.
- My handwritten notes (my handwriting is... not great)
- Typed equations from problem sets
- Textbook scans and photos
- Accuracy: Did it solve the problem right?
- Explanation Clarity: Could I follow the steps, or did it just give an answer?
- Practical Value: Did it help me actually understand DEs, or was it just a shortcut?
- Handles typed & handwritten problems (even from old textbooks)
- Accurate with complex notations-way better than most OCR
- Gives you steps for almost all undergrad-level ODEs and many PDEs
- Free version only lets you scan about 50 problems a month
- Sometimes misses super-advanced PDEs or custom notations
- Interface is basic-no pretty graphs or animations
- Handles a huge range: ODEs, PDEs, Laplace, Fourier, boundary value problems
- Super powerful symbolic and numeric solver
- Up-to-date and trustworthy-I’ve never seen it make a basic math error
- You need WolframAlpha Pro ($5.49/month) to see full steps
- Interface can feel overwhelming-lots of info, not always beginner-friendly
- Sometimes skips little algebraic steps, which can confuse you if you’re new
- Best-in-class step-by-step explanations
- Clean, student-friendly interface
- Focuses on actually teaching you, not just giving the answer
- Only does ODEs, not PDEs or most boundary value problems
- Need Pro ($7.99/month) for full solutions
- Free version has ads, which can get annoying during a study marathon
- Always free
- Accepts handwriting, typed, and photo input
- Fast answers for common DEs
- Only handles basic ODEs
- Explanations are minimal or missing for DEs
- Can’t do complex, multi-step problems like PDEs or Laplace transforms
- Free
- Recognizes problems from photos
- Shows visual resources and web links
- No step-by-step DE solving
- Can’t handle complex problems or systems
- Not focused on higher-level math
- ApexVision AI: I tested this on some integrals and ODEs. It’s improving fast-especially good for detailed, conversational explanations if you want to “talk through” a problem.
- GeoGebra CAS Calculator: Great for visualizing slope fields and phase portraits.
- Photomath: Only handles very basic DEs, but awesome for algebra and calculus.
- Desmos: Perfect for plotting solutions and checking qualitative behavior of differential equations.
- Handwritten or scanned problems: Go with Mathpix-nothing else is as accurate.
- Need comprehensive coverage (PDEs, Laplace, transforms): WolframAlpha is the most complete and authoritative.
- Want to learn each step for ODEs: Symbolab explains best, hands down.
- Quick checks for simple problems: Microsoft Math Solver is free and fast.
- Struggling with concepts, not just the math: Socratic or ApexVision AI can help you understand, not just solve.
- Use Mathpix for handwritten homework and textbook scans.
- Use Symbolab when I’m stuck on a specific DE method and need to see every detail.
- Use WolframAlpha for advanced problems, boundary value problems, or anything with weird conditions.
- Double-check simple answers with Microsoft Math Solver before class.
Comparison Table
Here’s the quick comparison I wish I’d had before spending money:
| Tool | Best For | Step-by-Step Explanations | Supports All DE Types | Price |
|---|---|---|---|---|
| Mathpix | Handwritten & scanned problems | Yes | Yes (ODEs & PDEs) | Free tier, then $4.99/mo+ |
| WolframAlpha | Comprehensive solutions | Yes | Yes | Free basic, $5.49/mo Pro |
| Symbolab | Step-by-step learning | Yes | Mostly ODEs | Free limited, $7.99/mo Pro |
| Microsoft Math Solver | Quick, free answers | Partial | Basic ODEs | Free |
| Socratic by Google | Visual explanations | No | Basic ODEs | Free |
How I Tested These Tools
I’m not just listing features from the websites. Over three months, I took real homework problems-first- and second-order ODEs, systems, Laplace transforms, and some PDEs from my engineering textbook. I tested each AI using:
I rated each one for:
I even tried ApexVision AI for some bonus tests (more on that below).
Tool #1: Mathpix
When I’m grinding through homework and can’t type out ugly derivatives or integrals, Mathpix is my secret weapon. I literally snap a photo of my handwritten DE, and it turns it into neat LaTeX and solves it.
Where it shines: It’s the only tool I found that really “gets” messy handwriting and complicated textbook scans. I threw a second-order ODE at it: y'' - 3y' + 2y = 0. Even with sloppy numbers, Mathpix parsed it perfectly and gave me step-by-step solutions.
Pros:
Cons:
Pricing: Free for up to 50 scans a month, then $4.99/month for students.
Best for: Students with lots of handwritten notes or who work from printed textbooks.
Example from my homework: I had this system of ODEs from a circuits class. My photo wasn’t great, but Mathpix nailed it-and the step-by-step breakdown matched my professor’s solution. Saved me at least an hour.
Tool #2: WolframAlpha
WolframAlpha is legendary in math circles. I’ve used it since my first calculus class, and it’s still my go-to for any DE my professor throws at me.
Where it shines: I tested everything from simple first-order ODEs to Laplace transforms and boundary value problems. WolframAlpha handled almost everything I threw at it-ODEs, PDEs, systems, you name it. When I tried a Laplace transform problem from my controls class, it even gave me steps (once I paid for Pro).
Pros:
Cons:
Pricing: Free for basic answers, $5.49/month for steps and advanced features.
Best for: Comprehensive DE solving and higher-level coursework (engineering, physics, math majors).
Example from my homework: I had a partial differential equation (heat equation, classic) from physics. WolframAlpha not only solved it but let me tweak boundary conditions on the fly. Pro tip: If your professor gives you weird initial conditions, it’s the easiest tool for quick edits.
Tool #3: Symbolab
If you’re the student who wants to really learn the process-not just get the answer-Symbolab is a game changer. I used it to walk my friends through integrating factors and separation of variables. Nobody breaks down the steps better.
Where it shines: For ordinary DEs (first and second order), Symbolab gives you every transformation. I tried a nasty first-order nonhomogeneous ODE, and Symbolab explained every step-factoring, integrating, even plugging in the initial condition.
Pros:
Cons:
Pricing: Free limited, $7.99/month for full step-by-step breakdowns.
Best for: Students who want to understand and learn DE solving methods.
Example from my homework: My roommate kept missing the method of undetermined coefficients. Symbolab’s breakdown made it click-he finally understood why we guessed certain forms.
Tool #4: Microsoft Math Solver
If you need a quick, free answer for a basic ODE, Microsoft Math Solver will get the job done. I tried it on a simple y' + y = e^x, and it got the answer right away.
Where it shines: Speed and ease. Just snap, type, or scribble, and it solves. No steps for most advanced problems, though.
Pros:
Cons:
Best for: Checking simple homework or getting unstuck on easy DEs.
Example from my homework: I used it to double-check a textbook problem before class. Got the answer, but didn’t show any steps-so not great for learning, but useful in a pinch.
Tool #5: Socratic by Google
Socratic tries to explain math visually but isn’t designed for deep DE work. I scanned an ODE from my notes, and it recognized the problem, but just linked to web explanations-no actual solving or steps.
Where it shines: Visual explanations, connecting you to resources. Good if you want to understand the “big picture” but not for step-by-step DE solutions.
Pros:
Cons:
Best for: Reviewing basic concepts before tests or finding web tutorials fast.
Example from my homework: I snapped a photo of a second-order DE, and Socratic found a Khan Academy video explaining the general concept. Not helpful for solving, but good for review.
Related Tools I Tried
Here are a few more worth mentioning:
How to Choose the Right Tool for You
Here’s how I pick, depending on the problem:
Pro tip: Always try your actual homework in the free version before paying. I’ve seen tools ace textbook examples but totally miss weird wording or notation from real assignments.
Common mistake: Don’t assume every AI tool is equally good at every DE. For example, Symbolab is awesome for ODEs but can’t handle most PDEs.
FAQ
Which AI tool is best for solving PDEs?
WolframAlpha and Mathpix are your best bet. Most others, like Symbolab, focus only on ODEs-so check your specific problem first.
Can I use these AI tools for exam prep?
Absolutely. I used them to check my homework and understand tricky steps. Just make sure you practice solving DEs without AI too-your professor won’t let you use Mathpix on the final.
Are AI math solvers allowed in my class?
Check your syllabus or ask your professor. At my school, we could use them for homework but not during tests. (Hint: ApexVision AI has a great “explain this step” feature for studying without giving full answers.)
Do any of these tools explain every single step?
Symbolab gives the most detailed step-by-step breakdown for ODEs. Even WolframAlpha sometimes skips tiny algebra steps. Mathpix’s explanations are getting better but can be brief.
Are there free options that actually work for DEs?
Yes. WolframAlpha and Microsoft Math Solver are both free for basic ODEs, but you’ll need to pay for full step-by-step details or for tougher problems.
What Worked Best for My Classes
If I had to start over, here’s what I’d do:
And for explanations that actually make sense in plain English, I started using ApexVision AI whenever I needed a “tutor vibe” breakdown (super helpful for those midnight study sessions).
Final Thoughts
No AI is perfect at every type of differential equation-but these tools have saved me hours and helped me finally understand DEs, not just get through the homework. My biggest tip: Don’t be afraid to mix and match. Try the free versions, test them on your real assignments, and see which one helps you the most.
If you’re struggling with differential equations, don’t waste hours banging your head against the wall. The right AI can make these problems actually manageable-and maybe even a little fun.
Good luck, and happy solving!
