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}}

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

t a y l or ln (x), 3

in v erse l a pl a ce \frac{1}{( s + 2 ) ^{2}}

\frac{d y}{d x} = y x

\int_{0}^{3} 2 π (x) (3 x - x^{2}) d 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)}