# a mess of a diff eq

• Mar 6th 2008, 04:47 PM
dankelly07
a mess of a diff eq
almost got a solution to a differential equation, but wondering if anyone could help me tidy things up...

I have (int 1/(1+v^2)dv - (int v/(1+v^2)dv = ln(x)+C

which gives

arctan(v)-1/2ln(1+v^2)=ln(x)+C

Iam using v=y/x

is there any way of solving for y?? I thought of using exp but itll probz end up messy, what would be the general solution in this case?

another prob if anyones up for it,
an integral left from a dif eq...

int 1+v/((v-1)^2) dv .....
• Mar 6th 2008, 05:32 PM
TheEmptySet
Quote:

Originally Posted by dankelly07
almost got a solution to a differential equation, but wondering if anyone could help me tidy things up...

I have (int 1/(1+v^2)dv - (int v/(1+v^2)dv = ln(x)+C

which gives

arctan(v)-1/2ln(1+v^2)=ln(x)+C

Iam using v=y/x

is there any way of solving for y?? I thought of using exp but itll probz end up messy, what would be the general solution in this case?

another prob if anyones up for it,
an integral left from a dif eq...

int 1+v/((v-1)^2) dv .....

I don't think it can be solved for y...

As for your integral

$\frac{v+1}{(v-1)^2}=\frac{v-1+2}{(v-1)^2}=\frac{1}{v-1}+\frac{2}{(v-1)^2}$

This should help...