Question

Solve the differential equation (D4 + 16D2)y = x2 + 5

Answer 1

Given (D4 + 16D2)y = x2 + 5. …(1)

A.E., D4 + 16D2 = 0 i.e. D2 (D2 + 16) = 0

or D = 0, 0, ±4i … (2)

Thus, the complementary function,

C.F. = (c1 + c2x) + (c3cos 4x + c4 sin 4x) … (3)

For particular integral,

Hence complete solution becomes,

y = (c1 + c2x) + (c3 cos 4x + c4sin4x) + x2/64[x2/3 + 39/4]