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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d}{d x} (ln (x^{8} y))

\int_{0}^{1} x e^{5 x} d x

y^{^{''}} - 4 y^{^{'}} + 4 y = 4 - 8 t - (18 t e^{2 t} + 2 e^{2 t})

\int 2 \cdot x \cdot ln (x) d x

\frac{\partial}{\partial y} (- \frac{1}{2} x - 3 y + 1)

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