What is the solution for derivative of (dy/(dx))+5y=7 ?

The solution for derivative of (dy/(dx))+5y=7 is y=c_{1}cos(sqrt(5)x)+c_{2}sin(sqrt(5)x)+7/5

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derivative of (dy/(dx))+5y=7

\frac{d}{d x} (\frac{d y}{d x}) + 5 y = 7

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{7}{5}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 5 y = 7

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{7}{5}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{7}{5}

\frac{d}{d x} (e^{x} + e^{x + e^{- x}})

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What is the solution for derivative of (dy/(dx))+5y=7 ?
The solution for derivative of (dy/(dx))+5y=7 is y=c_{1}cos(sqrt(5)x)+c_{2}sin(sqrt(5)x)+7/5