Solve the differential equation by variation of parameters, subject to the initial conditions y(0) = 1, y'(0) = 0. 36y'' − y = xex/6

The homogeneous ODE

has characteristic equation

with roots at , and admits two linearly independent solutions,

as the Wronskian is

Variation of parameters has us looking for solutions of the form

such that

We have

and we get

The general solution is

The initial conditions tell us

so that the particular solution is

answer: a

step-by-step explanation:

if xy ~ yz therefore xy would be the same length as yz