# Thread: IVP, what am I doing wrong?

1. ## IVP, what am I doing wrong?

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:
-Matt

2. It looks like you just made one silly error.

$\displaystyle y' = \frac{y}{x} + \frac{7}{3} \frac{y^{3}}{x^{3}}$

3. 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 $\displaystyle c=-\frac{3}{14}$

4. It looks correct to me (except you're missing a negative sign inside of the radical). What answer is given in the book?

You can multiply the top and bottom by 3 and get the equivalent solution

$\displaystyle y(x) = \frac{3x}{\sqrt{9-42 \ln x}}$

5. Thank you! Yea, I forgot the negative... I am using webwork online so it tells me if the answer I put in is correct.