What is the solution for (d^2y)/(dx^2)+(dy)/(dx)=2e^x ?

The solution for (d^2y)/(dx^2)+(dy)/(dx)=2e^x is y=c_{1}+c_{2}e^{-x}+e^x

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(d^2y)/(dx^2)+(dy)/(dx)=2e^x

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = 2 e^{x}

y = c_{1} + c_{2} e^{- x} + e^{x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = 2 e^{x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + e^{x}

y = c_{1} + c_{2} e^{- x} + e^{x}

\int 5 e^{6 x} cos (e^{6 x}) d x

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 cos (2 t) e^{- t}

\frac{\partial}{\partial x} (sin (x^{2} - 9 x y))

\int \frac{1}{cos ^{5} ( x )} d x

2 y y^{^{'}} + 2 = y^{2} + 2 x, y (0) = 6

What is the solution for (d^2y)/(dx^2)+(dy)/(dx)=2e^x ?
The solution for (d^2y)/(dx^2)+(dy)/(dx)=2e^x is y=c_{1}+c_{2}e^{-x}+e^x