Test #1 Review: 2-SeparableEquations: Problem 1

$y^{\prime }=\frac{x^3}{y^5}$

rewrite in form:

$y^{\prime }+p(x)y=f(x)$

$y^{\prime }{y}^5=x^3$

Integrate both sides with respect to x:

$\int y^{\prime }{y}^{5}dx=\int x^{3}dx$

$\int \frac{dy}{dx}{y}^5\frac{dx}{1}=\int x^{3}dx$

$\int y^{5}dy=\int x^{3}dx$

implicit solution:

$\frac{y^6}{6}=\frac{x^4}{4}+c$