Chapter 9: First-Order Differential Equations - Section 9.2 - First-Order Linear Equations - Exercises 9.2 - Page 536: 8

$y=\dfrac{x^2}{e^{2x}}+\dfrac{c}{e^{2x}}$ or, $y=\dfrac{x^2+c}{e^{2x}}$

Re-write the given differential equation as: $e^{2x}y'+2e^{2x}y=2x$ Thus, we have $\int [e^{2x}y]' dx=\int 2x dx$ or, $e^{2x}y=x^2+c$ Hence, the General solution is: $y=\dfrac{x^2}{e^{2x}}+\dfrac{c}{e^{2x}}$ or, $y=\dfrac{x^2+c}{e^{2x}}$