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

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

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

y^{^{''}} + y = 5 x \cdot 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 \cdot 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}

3 x^{^{''}} + 48 x = 60 e^{- 4 t} cos (4 t)

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 2 e^{x}

- y^{^{''}} + y = e^{a \cdot x}, y (0) = 0, y (1) = 0

y^{^{''}} - 9 y = 9 e^{3} x - 6 x^{4}

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

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