What is the solution for y^{''}+16y=16cos(4x) ?

The solution for y^{''}+16y=16cos(4x) is y=c_{1}cos(4x)+c_{2}sin(4x)+2xsin(4x)

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y^{''}+16y=16cos(4x)

y^{^{''}} + 16 y = 16 cos (4 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) + 2 x sin (4 x)

Solution steps

y^{''} (x) + 16 y = 16 cos (4 x)

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) + 2 x sin (4 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) + 2 x sin (4 x)

f (x) = 2 π

\int_{x^{5}}^{x^{3}} (2 t - 1)^{3} d t

\frac{1}{e ^{5 - 2 x}}

\int 7 x e^{9 x} d x

f (x) = 2 x^{3} + 36 x^{2} + 192 x + 13

What is the solution for y^{''}+16y=16cos(4x) ?
The solution for y^{''}+16y=16cos(4x) is y=c_{1}cos(4x)+c_{2}sin(4x)+2xsin(4x)