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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} - 1 = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2} \cdot e^{(- 2 x)} + 1

y^{^{''}} - 2 y^{^{'}} + y = x^{2}, y (0) = 2, y^{^{'}} (0) = 2

y^{^{''}} - y = sin (t), < y (0) = 0, y^{^{'}} (0) = 1

5 y^{^{''}} + y^{^{'}} = - 2 x, y (0) = 0, y^{^{'}} (0) = - 20

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