$1\mathrm{.}5$ Other Methods $-$ Substitution: Problem $2$

$(2$ points$)$

Use the substitution $z=\frac{y}{x}$ to solve the initial value problem $y^{\text{'}}=\frac{x^2-y^2}{xy}$ with $y(2)=4$

Give an explicit solution in the form $y=f(x).$

help $($equations$).$

Hint: Be careful to satisfy the initial condition when taking square roots or simplifying absolute values$\mathrm{.}1\mathrm{.}5$ Other Methods $-$ Substitution: Problem $2$

$(2$ points$)$

Use the substitution $z=\frac{y}{x}$ to solve the initial value problem $y^{\text{'}}=\frac{x^2-y^2}{xy}$ with $y(2)=4$

Give an explicit solution in the form $y=f(x).$

help $($equations$).$

Hint: Be careful to satisfy the initial condition when taking square roots or simplifying absolute values.