DiffEqHomogeneous

2nd-Order Constant Coefficient ODE (Homogeneous)

Solve ay″ + by′ + cy = 0 using the characteristic equation ar² + br + c = 0.

Live Calculator · Step-by-Step · Differential Equations

Inputs

a (y″)

b (y′)

c (y)

Initial Condition y(0) = y₀

Initial Condition y′(0) = y₁

Results

Characteristic Equation

—

Discriminant D = b² − 4ac

—

Roots

—

General Solution

—

Particular Solution (with ICs)

—

Step-by-Step Work

Your solution will appear here.

Solution y(x) on [0, 10]