What is the solution for y^'+y=yxe^{x+2} ?

The solution for y^'+y=yxe^{x+2} is y=e^{e^2(e^xx-e^x)-x+c_{1}}

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y^'+y=yxe^{x+2}

y^{^{'}} + y = y x e^{x + 2}

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

Solution steps

y^{'} (x) + y = y x e^{x + 2}

Solve separable ODE:

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

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

\int \frac{x}{3 x + 4} d x

x \to 3 lim (\frac{1}{( x - 3 ) ^{8}})

x \to - 3 lim (\frac{x ^{2} - 9}{3 + x})

\frac{d}{d x} (\frac{2}{3 x ^{\frac{1}{3}}})

\int_{3}^{5} \frac{x}{x ^{2} - 3} d x

What is the solution for y^'+y=yxe^{x+2} ?
The solution for y^'+y=yxe^{x+2} is y=e^{e^2(e^xx-e^x)-x+c_{1}}