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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

e^{- x^{2}} (1 - 2 x^{2})

x \to 6 + lim (x^{3} + c x)

f (x) = x + x x

ln (x), 3

x \to 6 lim (h (x))

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