Differential Equations Calculator
Solve ordinary differential equations (ODEs) with step-by-step solutions and slope field visualization
Differential Equation Setup
Supported separable equations: y, x, x*y, x/y. Enter only the right-hand side.
Slope Field Visualization
Each small line segment shows the slope dy/dx at that point. The orange dot shows your initial condition.
Theory & Formula
Differential Equations
A differential equation relates a function to its derivatives. First-order ODEs have the form dy/dx = f(x,y). The solution is a function y(x) that satisfies this relationship.
Separable Equations
A separable equation can be written as a product of functions of x and y. We can separate variables and integrate both sides:
\(\frac{dy}{dx} = g(x)h(y) \implies \frac{dy}{h(y)} = g(x)\,dx\)Example: Solve dy/dx = y
\(\frac{dy}{dx} = y\)\(\frac{dy}{y} = dx\)\(\int \frac{dy}{y} = \int dx\)\(\ln|y| = x + C_1\)\(y = Ce^x\)
Initial Value Problems
An initial value problem (IVP) specifies both a differential equation and an initial condition y(x₀) = y₀. This determines a unique particular solution.