Differential Equation Calculator

Solve differential equations step-by-step with detailed solutions for separable, linear, homogeneous, exact, Bernoulli, and second-order equations

Example Equations

Equation Type

dy/dx = f(x)g(y)

Equation

Example: dy/dx = x*y

Apply Initial Condition

Solution Method:

Separation of variables

Separable: dy/dx = f(x)g(y)

Variables can be separated to different sides

Linear First Order: dy/dx + P(x)y = Q(x)

Solved using integrating factor method

Homogeneous: dy/dx = f(y/x)

Use substitution v = y/x

Exact: M(x,y)dx + N(x,y)dy = 0

When ∂M/∂y = ∂N/∂x

Bernoulli: dy/dx + P(x)y = Q(x)y^n

Use substitution v = y^(1-n)

•

Select the type of differential equation from the dropdown

•

Enter your equation using standard notation (dy/dx, y', y'')

•

Optionally add initial conditions for particular solutions

•

Review the step-by-step solution and verify the result

•

Copy the complete solution report for your records