• Nov 14th 2007, 03:00 PM
berkanatci

1)y.y'' + 3(y')^2=0 this is differential equation.find the solution.???

2)x'=q - 12 + 3x - x^3 q is a bifurcation point.Draw the bifurcation diagram

3)a)show that any linear 1st order dif. eq. can be writen as a total differential?
b)obtain 'that' total dif ?

thank you so much.....again
• Nov 14th 2007, 05:47 PM
ThePerfectHacker
Quote:

Originally Posted by berkanatci

1)y.y'' + 3(y')^2=0 this is differential equation.find the solution.???

You can write,
$\displaystyle y\cdot y'' = -3y' \cdot y'$
Assuming $\displaystyle y$ does not vanish on $\displaystyle (-\infty,\infty)$:
$\displaystyle \frac{y''}{y'} = \frac{-3y'}{y}$.
Thus,
$\displaystyle \int \frac{y''}{y'} dx = \frac{-3y'}{y} dx + C$.
That means,
$\displaystyle \ln |y'| = -3\ln |y| + C$
Thus,
$\displaystyle \ln |y'| = \ln |y|^{1/3} + C$
Thus,
$\displaystyle \ln |y'| - \ln |y|^{1/3} = C$
Thus,
$\displaystyle \ln \left| \frac{y'}{y^{1/3}}\right| = C \implies \frac{y'}{y^{1/3}} = C \mbox{ where }C\not = 0$.
Now this is a basic equation which is seperable.
• Nov 14th 2007, 09:41 PM
berkanatci
thank you so much man.maybe you will survive in my life....because it is exam question....thank you again