Verify that the given functions y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. t2y'' − 2y = 5t2 − 1, t > 0, y1(t) = t2, y2(t) = t−1

satisfies given homogenous solution and the particular solution is .

Step-by-step explanation:

Given homogeneous equation is,

where t>0 subject to

To verify,

Thus and satisfies (1).

Now the wronskean,

Thus and are solution of (1) .

     where

    sincce

Hence the result.

. + λrh() e 1 1 2 4 4 4 4 4 3 4 4 4 4 4 + th−1(− s(x)2 dx ω + λrh−1() e 2 1 2 4 4

step-by-step explanation: