M
MJJ Tools

Differential Equation Calculator

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

Example Equations

Differential Equation

dy/dx = f(x)g(y)
Example: dy/dx = x*y
Solution Method:
Separation of variables

Solution

Equation Types

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)

How to Use

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