The initial value problem [frac{d y}{d x}=frac{y^{2}+x y}{x^{2}}, quad y(1)=1] does not fall into the class of

Question:

The initial value problem

\[\frac{d y}{d x}=\frac{y^{2}+x y}{x^{2}}, \quad y(1)=1\]

does not fall into the class of problems considered in this chapter. However, if one substitutes $y(x)=x z(x)$ into the differential equation, one obtains an equation for $z(x)$ that can be solved. Use this substitution to solve the initial value problem for $y(x)$.

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