What is the solution for e^x(dy)/(dx)+2e^xy=1 ?

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

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e^x(dy)/(dx)+2e^xy=1

e^{x} \frac{d y}{d x} + 2 e^{x} y = 1

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

Solution steps

e^{x} \frac{d y}{d x} + 2 e^{x} y = 1

Solve linear ODE:

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

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

\frac{d}{d x} (c_{1} e^{- 2 x} + c_{2} x e^{- 2 x})

f (x) = e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x}

\int \frac{1}{( 5 - 4 x - x ^{2} ) ^{\frac{5}{2}}} d x

\int \frac{1}{cos ( x ) + sin ( x )} d x

\frac{5}{( s + 2 ) ^{4}}

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