DIFFERENTIAL EQUATIONS

Question

Verify that y₁(x) is indeed a solution and find a second linearly independent solution by reduction of order. 

(i) y`` − 2y` + y = 0, y₁(x) = e^x 

(ii) y`` + 4y = 0, y₁(x) = sin 2x

 (iii) y`` − 4y = 0, y₁(x) = e^(2x)