Chapter 9: First-Order Differential Equations - Section 9.2 - First-Order Linear Equations - Exercises 9.2 - Page 537: 20

$y=1-7e^{-x^2/2}$

Here, we have $y'+xy=x$ The integrating factor is: $I=e^{\int xdx}=e^{x^2/2}$ Now, $e^{x^2/2}[y'+xy]=e^{x^2/2}x$ This gives: $\int ye^{x^2/2}=\int e^{x^2/2} x$ or, $y=1+ce^{-x^2/2}$ After applying the initial conditions, we have $ c=-7$ So, $y=1+ce^{-x^2/2} \implies y=1-7e^{-x^2/2}$