The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula below:

y2 = y1(x) ∫ [e^(−∫P(x) dx)/ y²₁(x)]dx
as instructed, to find a second solution y2(x).
y'' − 4y' + 4y = 0; y1 = e^(2x)
y2 =?

Given is a fundamental solution, we posit a second solution of the form , with derivatives

Substitute these into the ODE:

Integrate both sides twice to get

Then the second fundamental solution is

but already cover , so .

d

step-by-step explanation:

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