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

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

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x(dy)/(dx)+(2x+1)y=xe^{-2x}

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

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

Solution steps

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

Solve linear ODE:

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

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

\int \frac{x ^{2}}{x - 2} d x

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x \to 0 + lim (x cot (x) csc (x))

x^{4}, at x = 3

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