DiffEqReduction of Order

Reduction of Order — Finding a Second Solution

Given one solution y₁ of y″ + P(x)y′ + Q(x)y = 0, find y₂ = v(x)y₁ by substituting and solving the resulting first-order equation.

Live Calculator · Step-by-Step · Differential Equations

Inputs

Equation & Known Solution y₁

Results

Known Solution y₁

—

Reduction Substitution

—

Second Solution y₂

—

Wronskian W(y₁,y₂)

—

General Solution

—

Step-by-Step Work

Your solution will appear here.

Solutions y₁(x) and y₂(x) on [0.5, 5]

Put It Into Practice

The calculator shows the steps — a quiz proves you can do them on your own.

Alexander tutors all math and CS levels — $55/session, free consultation.