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

The solution for (dy)/(dx)=-2y+e^x is y=(e^x)/3+(c_{1})/(e^{2x)}

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

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

y = \frac{e ^{x}}{3} + \frac{c _{1}}{e ^{2 x}}

Solution steps

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

Solve linear ODE:

y = \frac{e ^{x}}{3} + \frac{c _{1}}{e ^{2 x}}

y = \frac{e ^{x}}{3} + \frac{c _{1}}{e ^{2 x}}

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What is the solution for (dy)/(dx)=-2y+e^x ?
The solution for (dy)/(dx)=-2y+e^x is y=(e^x)/3+(c_{1})/(e^{2x)}