Standard table.
AskSia recognizes functions as known table entries and writes the transform directly.
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Laplace Transform Solver
Laplace transforms, forward and inverse.
Type or photograph the function or its transform. AskSia uses the standard table, the first and second shift theorems, the derivative-of-transform rule, and partial fraction decomposition. Initial-value problems with piecewise forcing 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
What is a Laplace transform?
The Laplace transform turns a function f(t) into a function F(s) of a complex variable, defined by an integral from 0 to infinity. It is useful for solving initial-value problems: the transform converts derivatives into multiplications by s, turning differential equations into algebraic ones. After solving in s, the inverse transform recovers the time-domain answer. Standard pairs (e^(at), sin, cos, t^n) are tabulated, and the shift theorems handle modifications.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Laplace.
Every step transparent, every answer self-checked.
Shift theorems.
First shift (e^(at)*f(t)) and second shift (step-function * f(t-a)) handled automatically.
Shifts
Partial fractions.
For inverse transforms of rational F(s), AskSia decomposes and inverse-transforms each piece.
Partial fractions
Initial-value problems.
ODEs with initial conditions transformed, solved in s, and inverse-transformed back to t.
IVP
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 Laplace 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 Laplace solver covers.
Standard functions.
Transforms of e^(at), sin(omega*t), cos(omega*t), t^n. Direct from table.
Table
Piecewise forcing.
Step functions u(t-a) and impulses delta(t-a). Use second shift.
Piecewise
Inverse transforms.
F(s) given, find f(t). Partial fractions and shift theorems.
Inverse
Differential equations.
y'' + 3y' + 2y = e^(-t) with y(0) = 0. Transform, solve, inverse-transform.
ODE
Resonance and oscillation.
Spring-mass-damper systems. AskSia handles the algebra in s.
Engineering
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.
When are Laplace transforms most useful?
For initial-value problems in linear ODEs with constant coefficients, especially when the forcing term is discontinuous or piecewise (step functions, impulses). The transform turns derivatives into algebra, the algebraic equation gets solved cleanly, and the inverse transform recovers the time-domain solution.
What is the first shift theorem?
It says the Laplace transform of e^(at) * f(t) equals F(s - a), where F(s) is the transform of f(t). So multiplying by an exponential in time shifts the transform variable. AskSia detects exponential multipliers and applies this theorem automatically to compute the transform or invert it.
How does AskSia handle partial fractions in s?
For an inverse transform with rational F(s) = P(s)/Q(s), AskSia factors Q(s), sets up the partial fraction decomposition with appropriate forms for each factor type (linear, repeated, irreducible quadratic), solves the resulting linear system for the coefficients, and inverse-transforms each piece using the standard table.
Can Laplace solve systems of ODEs?
Yes. For coupled linear systems, take the transform of each equation, getting a system of algebraic equations in the transforms of each unknown function. Solve the algebraic system, then inverse-transform each component. AskSia handles 2-by-2 and 3-by-3 systems this way.
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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Transform, solve in s, transform back.
Join 2M+ students using AskSia to solve laplace problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.
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