Classified first.
Order, linearity, separability, exactness all identified before any integration.
Type-aware
AI Solver by AskSia
Ordinary Differential Equation Solver: solved cleanly
Type or photograph your ODE. AskSia identifies whether it is separable, linear, exact, Bernoulli, or second-order with constant coefficients, then applies the right method. Initial-value problems supported.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
98% · Verified
Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
How do you solve an ordinary differential equation?
To solve an ordinary differential equation (ODE), first classify it by order and structure. First-order separable: collect y terms on one side, x terms on the other, integrate. First-order linear: use the integrating factor e^(integral P dx). First-order exact: find a potential function. Second-order linear constant-coefficient: solve the characteristic equation and write the general solution from the roots. Initial conditions give particular constants.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Ordinary Differential Equation.
Every step transparent, every answer self-checked.
Method per type.
Each ODE type has its method. AskSia picks correctly and explains the choice.
Method
Step-by-step integration.
Every integration shown with the technique, the antiderivative, and the constant of integration.
Step-by-step
General to particular.
General solution with arbitrary constants. Initial conditions narrow to a particular solution.
Complete
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support.
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework.
Self-checked
How It Works
Solve any Ordinary Differential Equation problem in three steps.
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Ordinary Differential Equation solver covers.
Separable.
dy/dx = x*y. Separate, integrate.
Separable
Linear first-order.
dy/dx + 2y = e^x. Integrating factor e^(2x).
Linear
Homogeneous second-order.
y'' - 5y' + 6y = 0. Characteristic equation gives general solution.
Homogeneous
Non-homogeneous.
y'' + y = sin(x). Undetermined coefficients or variation of parameters.
Non-homogeneous
Word problems.
Newton's cooling, mixing tanks, exponential growth/decay all give first-order ODEs.
Applications
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value.
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
What is the difference between general and particular solutions?
The general solution contains arbitrary constants (one for each order). It represents the family of all solutions. A particular solution comes from applying initial or boundary conditions to fix the constants, picking out one specific member of the family.
How does the characteristic equation work?
For a second-order linear constant-coefficient homogeneous ODE ay'' + by' + cy = 0, substitute y = e^(rx). This gives ar^2 + br + c = 0, the characteristic equation. The roots determine the form of the general solution: distinct real roots give exponentials, repeated roots give x*e^(rx), complex roots give sines and cosines wrapped in an exponential.
Can AskSia handle non-constant coefficient ODEs?
Some. Cauchy-Euler equations (ax^2 y'' + bx y' + cy = 0) reduce to constant-coefficient via a substitution. Other variable-coefficient ODEs may have closed-form solutions only in special cases. For general variable-coefficient ODEs without closed forms, AskSia uses series methods or numerical methods.
What is an exact ODE?
An exact ODE M(x, y) dx + N(x, y) dy = 0 has the property that there exists a function F(x, y) with dF/dx = M and dF/dy = N. The solution is F(x, y) = C. AskSia checks the exactness condition (dM/dy = dN/dx), finds the potential function F by partial integration, and writes the implicit solution.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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Join 2M+ students using AskSia to solve ordinary differential equation problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.
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