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Solve the differential equation (D^4 + 16D^2)y = x^2 + 5

+1 vote

asked Oct 18, 2018 in JEE by kratos

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

jee
differential equations
jee mains
undetermined coefficient
class-12

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1 Answer

+1 vote

answered Feb 22, 2020 by kratos

Best answer

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) + (c3cos4x + c4sin4x) … (3)

For particular integral,

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