What is the solution for y^{''}+y=7xsin(x) ?

The solution for y^{''}+y=7xsin(x) is y=c_{1}cos(x)+c_{2}sin(x)-(7x^2cos(x))/4+(7xsin(x))/4

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y^{''}+y=7xsin(x)

y^{^{''}} + y = 7 x sin (x)

y = c_{1} cos (x) + c_{2} sin (x) - \frac{7 x ^{2} cos ( x )}{4} + \frac{7 x sin ( x )}{4}

Solution steps

y^{''} (x) + y = 7 x sin (x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - \frac{7 x ^{2} cos ( x )}{4} + \frac{7 x sin ( x )}{4}

y = c_{1} cos (x) + c_{2} sin (x) - \frac{7 x ^{2} cos ( x )}{4} + \frac{7 x sin ( x )}{4}

y^{^{''}} - 2 y^{^{'}} = x + 1

y^{^{'''}} + y^{^{'}} = 3 + cos (x) - sin (x) + x

y^{^{''}} - y = e^{- 2 x} sin (e^{- x})

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 91 x e^{x}

x^{^{''}} + x = sin^{2} (t)

What is the solution for y^{''}+y=7xsin(x) ?
The solution for y^{''}+y=7xsin(x) is y=c_{1}cos(x)+c_{2}sin(x)-(7x^2cos(x))/4+(7xsin(x))/4