What is the solution for y^{''}+25y=2xcos(x) ?

The solution for y^{''}+25y=2xcos(x) is y=c_{1}cos(5x)+c_{2}sin(5x)+(xcos(x))/(12)+1/144 sin(x)

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y^{''}+25y=2xcos(x)

y^{^{''}} + 25 y = 2 x cos (x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x cos ( x )}{12} + \frac{1}{144} sin (x)

Solution steps

y^{''} (x) + 25 y = 2 x cos (x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x cos ( x )}{12} + \frac{1}{144} sin (x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x cos ( x )}{12} + \frac{1}{144} sin (x)

y^{^{''}} + 4 y = sec^{3} (2 t)

12 \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 y = e^{x}

y^{^{''}} + 4 y = 16 t, y (0) = 3, y^{^{'}} (0) = - 6

y^{^{''}} - 4 y = 2

y^{^{''}} - 3 y^{^{'}} + 2 y = 9 e^{3 x}

What is the solution for y^{''}+25y=2xcos(x) ?
The solution for y^{''}+25y=2xcos(x) is y=c_{1}cos(5x)+c_{2}sin(5x)+(xcos(x))/(12)+1/144 sin(x)