Answer
$y=\dfrac{x^2}{e^{2x}}+\dfrac{c}{e^{2x}}=\dfrac{x^2+c}{e^{2x}}$
Work Step by Step
The standard form of the given equation is:
$e^{2x}y'+2e^{2x}y=2x$ ....(1)
In order to determine the general solution, multiply equation (1) with the integrating factor and integrate both sides.
$\int [e^{2x}y]' dx=\int 2x dx$
or, $e^{2x}y=x^2+c$
Thus, the general solution is as follows:
$y=\dfrac{x^2}{e^{2x}}+\dfrac{c}{e^{2x}}=\dfrac{x^2+c}{e^{2x}}$
