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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d y}{d x} x - x e^{x} + y = 0

\frac{d y}{d x} = x + 1

y^{^{'}} = \frac{3 y}{x}

\frac{( 10 s + 8 )}{s ^{3}}

x \to 0 lim (\frac{c}{x})

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