First order differential equations (integrating factor)
1
Find the general solution of the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + x y = x \mathrm { e } ^ { \frac { 1 } { 2 } x ^ { 2 } }$$
giving your answer in the form \(y = \mathrm { f } ( x )\).
Find the particular solution for which \(y = 1\) when \(x = 0\).