What is the solution for y^{''}+25y=3sin(5x) ?

The solution for y^{''}+25y=3sin(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)-(3xcos(5x))/(10)

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y^{''}+25y=3sin(5x)

y^{^{''}} + 25 y = 3 sin (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) - \frac{3 x cos ( 5 x )}{10}

Solution steps

y^{''} (x) + 25 y = 3 sin (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) - \frac{3 x cos ( 5 x )}{10}

y = c_{1} cos (5 x) + c_{2} sin (5 x) - \frac{3 x cos ( 5 x )}{10}

y^{^{''}} + 4 y = 9 t, y (0) = 0, y (0) = 7

y^{^{''}} + 16 y = 4 x, y (0) = 1, y^{^{'}} (0) = 4

y^{^{''}} + 5 y^{^{'}} = 15 x^{2}

y^{^{'''}} - y^{^{'}} = x + 1

(D - 1) y = 2 sin (5 t), y (0) = 0

What is the solution for y^{''}+25y=3sin(5x) ?
The solution for y^{''}+25y=3sin(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)-(3xcos(5x))/(10)