Category: Student Work (Page 25 of 44)

$y’=\frac{x^3}{y^5}$

rewrite in form:

$y’+p(x)y=f(x)$

$y’y^5=x^3$

Integrate both sides with respect to x:

$\int y’ y^5 dx = \int x^3 dx$

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

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

implicit solution:

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

I had to place it as a pdf file because openlab for some reason makes my images blurry