# DE question

1. Nov 24, 2008

### -Vitaly-

1. The problem statement, all variables and given/known data
Solve:

2. Relevant equations
DE stuff

3. The attempt at a solution
I started by doing substitution: x=U+3/2 and y=W-1/2

So, it gave me , but , so .

Therefore,

And, . Substitution z=W/U. Giving, (*).

And,

Rearranging gives . Substitute in (*)

=> =>

Dividing 1/(1+z2) and -z/(1+z2) and integrating gives:

. But now I'm stuck :( because I can't solve this for z and go back to y and x :( maybe I made an arithmetical mistake or maybe there is a better method?
Thank you

Last edited: Nov 24, 2008
2. Nov 24, 2008

### µ³

I don't know how correct the method you detailed is but a lot of times for a differential equation, an implicit solution is sufficient.

3. Nov 25, 2008

### -Vitaly-

Surely there is a way to solve it explicitely

4. Nov 25, 2008

### HallsofIvy

Staff Emeritus
Why "surely". You don't need to solve
$$arctan z-\frac{1}{2}ln(z^2+ 1)= ln(U)+ C$$

z= W/U so that is
$$arctan W/U-\frac{1}{2}ln(\frac{W^2}{U^2}+ 1)= ln(U)+ C$$
and U= x- 3/2, W= y+ 1/2 so
$$arctan\frac{y+ 1/2}{x-3/2}- \frac{1}{2}ln(\frac{(y+1/2)^2}{(x-3/2)^2}= ln(x- 3/2)+ C$$
That's a perfectly good solution. (Assuming your integration was correct.)