First order differential equations (integrating factor)
7
Use the substitution \(\mathrm { u } = 1 + \mathrm { x } ^ { 2 }\) to find
$$\int \frac { x } { \sqrt { 1 + x ^ { 2 } } } d x$$
Find the solution of the differential equation
$$x \frac { d y } { d x } - y = x ^ { 2 } \sinh ^ { - 1 } x$$
given that \(y = 1\) when \(x = 1\). Give your answer in the form \(\mathrm { y } = \mathrm { f } ( \mathrm { x } )\).