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

The solution for y^{''}+y=5xsin(x) is y=c_{1}cos(x)+c_{2}sin(x)-(5x^2cos(x))/4+(5xsin(x))/4

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y^{''}+y=5xsin(x)

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

y = c_{1} cos (x) + c_{2} sin (x) - \frac{5 x ^{2} cos ( x )}{4} + \frac{5 x sin ( x )}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - \frac{5 x ^{2} cos ( x )}{4} + \frac{5 x sin ( x )}{4}

y = c_{1} cos (x) + c_{2} sin (x) - \frac{5 x ^{2} cos ( x )}{4} + \frac{5 x sin ( x )}{4}

y^{^{''}} - y^{^{'}} - 2 y = cosh (2 t)

y^{^{''}} - y = sin (x)

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- t}, y (4) = 1, y^{^{'}} (4) = 3

y^{^{''}} + 25 y = 2 x cos (5 x)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 y = 3 cos (x)

What is the solution for y^{''}+y=5xsin(x) ?
The solution for y^{''}+y=5xsin(x) is y=c_{1}cos(x)+c_{2}sin(x)-(5x^2cos(x))/4+(5xsin(x))/4