1. ## homogenous differential equation

why my ans is different from the ans given , the ans given is 1 +4(y/x ) - 3 (( y/x) ^2 ) = 1/(c x^2) ? which part of my working is wrong ?

2. ## Re: homogenous differential equation

From $\displaystyle x{\mathrm d v \over \mathrm d x}={1+4v-3v^2 \over 3v-2}$ you should go to $\displaystyle {3v-2 \over 1+4v-3v^2}{\mathrm d v \over \mathrm d x}=\frac1x$. Then use partial fractions to integrate

3. ## Re: homogenous differential equation

Originally Posted by Archie
From $\displaystyle x{\mathrm d v \over \mathrm d x}={1+4v-3v^2 \over 3v-2}$ you should go to $\displaystyle {3v-2 \over 1+4v-3v^2}{\mathrm d v \over \mathrm d x}=\frac1x$. Then use partial fractions to integrate
how to make it into partial fraction ? for -3(v^2) +4v +1 , i gt v=1.55 , -0.215 , i cant get whole number . tat's weird

4. ## Re: homogenous differential equation

$\displaystyle {3v-2 \over 1+4v-3v^2}=-\frac12 {4-6x \over 1+4v-3v^2} = -\frac12 {{\mathrm d \over \mathrm d x}( 1+4v-3v^2) \over 1+4v-3v^2}$

5. ## Re: homogenous differential equation

Originally Posted by Archie
$\displaystyle {3v-2 \over 1+4v-3v^2}=-\frac12 {4-6x \over 1+4v-3v^2} = -\frac12 {{\mathrm d \over \mathrm d x}( 1+4v-3v^2) \over 1+4v-3v^2}$
how to make 2v -2 into ( -1/2 )(4- 6x) ??

6. ## Re: homogenous differential equation

Well, you can't make 2v- 2 into (-1/2)(4- 6x)! But you can make it into (-1/2)(4- 6v) by factoring out -1/2. Frankly, your basic problem in all of these problems you have posted is that your algebra is very weak. And that is a real problem in differential equations! Review and practice algebra.

7. ## Re: homogenous differential equation

Originally Posted by HallsofIvy
Well, you can't make 2v- 2 into (-1/2)(4- 6x)! But you can make it into (-1/2)(4- 6v) by factoring out -1/2. Frankly, your basic problem in all of these problems you have posted is that your algebra is very weak. And that is a real problem in differential equations! Review and practice algebra.
i still dont understand , can you explain further ?
i have redo the question , i reached here now , but still didnt get the answer