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ODE Solver
ODEs, the right method on each one.
Type or photograph the ODE. AskSia classifies it (first-order separable, linear, exact, Bernoulli; second-order constant-coefficient; Laplace-amenable IVP), picks the method, integrates step-by-step, and returns the general solution with initial-value work and interval of validity.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
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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
What is an ODE?
An ordinary differential equation (ODE) is an equation relating a function and its derivatives, where the function depends on a single variable. The order is the highest derivative present. Solution methods depend on the type: first-order ODEs can be separable, linear (use integrating factor), exact, or Bernoulli. Second-order linear ODEs with constant coefficients use the characteristic equation. Initial-value problems with discontinuous forcing often use Laplace transforms.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for ODE Differential Equation.
Every step transparent, every answer self-checked.
Right method.
Integrating factor for first-order linear, characteristic equation for second-order, Laplace for IVP with piecewise forcing.
Method
General and particular.
General solution with arbitrary constants, then particular from initial conditions.
Complete
Substitution check.
AskSia plugs the solution back into the ODE to verify it satisfies the equation.
Verified
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 ODE 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
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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
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Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the ODE Differential Equation solver covers.
Separable first-order.
dy/dx = f(x)g(y). Separate variables, integrate both sides.
First-order
Linear first-order.
dy/dx + P(x)y = Q(x). Compute integrating factor, integrate.
First-order
Second-order homogeneous.
ay'' + by' + cy = 0. Solve characteristic equation, write general solution.
Second-order
Non-homogeneous.
Right-hand side nonzero. Find particular solution by undetermined coefficients or variation of parameters.
Non-homogeneous
IVP by Laplace.
y'' + y = f(t) with y(0), y'(0) given. Transform, solve in s, inverse-transform.
Laplace IVP
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.
How does AskSia classify an ODE?
It looks at the order, linearity, and structure. The classification determines which method applies. AskSia names the type at the top of the solution so you understand why a particular technique was used.
What is the integrating factor method?
For a first-order linear ODE dy/dx + P(x)y = Q(x), the integrating factor is mu(x) = e^(integral P(x) dx). Multiply both sides by mu, and the left side becomes d/dx of (mu * y). Integrate both sides to get mu*y, then divide by mu to solve for y.
When does AskSia use Laplace transforms?
Laplace is the cleanest method for initial-value problems where the forcing term is discontinuous, piecewise, or includes impulses or step functions. For homogeneous equations or simple polynomial forcing, the characteristic equation is faster. AskSia picks the cleanest method.
Can AskSia solve systems of ODEs?
Yes, for 2-equation and 3-equation linear systems with constant coefficients. AskSia builds the coefficient matrix, finds eigenvalues and eigenvectors, and writes the general solution in matrix-exponential form.
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. 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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Classification, method, integration, verification.
Join 2M+ students using AskSia to solve ode differential equation problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.
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