Hi, I am trying to solve a differential ivp and I can't seem to get the correct answer. The homogeneous differential equation is: $\displaystyle 3x^2y+7y^3-3x^3y'=0, y(1)=1$ Here is my work:
Thanks for your time!
-Matt
Ah, thank you! But I am still not getting the right answer.
After the integration:
$\displaystyle -\frac{3}{14v^2}=ln|x|+c$
$\displaystyle v^{-2}=-\frac{14}{3}ln|x|-\frac{14}{3}c$
$\displaystyle v=\frac{1}{\sqrt{\frac{14}{3}ln|x|-\frac{14}{3}c}}$
$\displaystyle \frac{y}{x}=\frac{1}{\sqrt{\frac{14}{3}ln|x|-\frac{14}{3}c}}$
$\displaystyle y=\frac{x}{\sqrt{\frac{14}{3}ln|x|-\frac{14}{3}c}}$
After the substitution for $\displaystyle y(1)=1$ I get $\displaystyle c=-\frac{3}{14}$