ODE Solver Calculator

📝 Practice worksheet
Type derivatives naturally: y', dy/dx, etc. (auto-translates to calculator syntax). Use y for y(x). Multiplication needs *: 2*x*y.
Preview type an ODE above…
Try one
More examples
ODE Reference Table
TypeFormMethod
Separable
1st Linear
Bernoulli
Exact
Homogeneous
2nd Const Coeff
Non-Homogeneous
Cauchy-Euler
3rd Const Coeff
4th Order (Beam)
Variable: y represents y(x).
Derivatives: y', y'', dy/dx, d²y/dx² (all auto-normalize) — or use yp, ypp, yppp, y4, y5 directly.
Functions: sin, cos, tan, exp, log, sqrt.
Powers / multiplication: x^2 or x**2; always use * (e.g. 2*x*y).
Constants: pi, e.
dy/dx

Ready when you are

Type an ODE above and hit Solve.

Solve an ODE to see its graph.

Frequently asked

Yes. Click the green 📷 Scan button next to the equation input, upload a photo or PDF of your homework, and our AI extracts every ODE on the page along with any initial conditions. Pick a problem to fill the form and solve. Works on textbook pages, exam papers, and handwritten work.
First identify the type: separable, linear, Bernoulli, exact, or homogeneous. Then apply the appropriate method. For separable ODEs, separate variables and integrate. For linear ODEs y' + P(x)y = Q(x), multiply by the integrating factor μ = e∫P dx. The calculator automatically classifies and solves first-order ODEs.
Yes. The calculator solves initial value problems (IVPs). For first-order: y(x₀) = y₀. For second-order: y(x₀) = y₀ and y'(x₀) = y'₀. Initial conditions determine the unique particular solution.
A direction field is a graphical representation of dy/dx = f(x, y). At each point a short line segment shows the slope f(x, y). The pattern reveals qualitative solution behaviour without solving analytically.
Separable, first-order linear, Bernoulli, exact, homogeneous, second-order constant coefficient (homogeneous and non-homogeneous), Cauchy-Euler, and many more. Auto-classification chooses the right method.
A general solution contains arbitrary constants (C₁, C₂, …) and represents all possible solutions. A particular solution applies initial conditions to fix those constants.
Yes — 100% free, no signup, no daily limits. Step-by-step solutions, ODE classification, verification, interactive graphs, direction field plots, AI photo scan, MathLive visual input, 1,000+ practice problems, and a built-in Python compiler.
Yes — over 1,000 ODE practice problems. Filter by 8+ question types and 4 difficulty levels. Each worksheet is randomly generated with a full answer key.