# PDE separation of variable problem

1. Oct 25, 2011

### JamesGoh

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

Using the method of separation of variables, obtain a solution of the following PDE subject to
the given conditions

$\frac{du}{dx}+y\frac{du}{dy}=(2x+y)u$

$u(x,1)=5e^{x^{2}-x}$

2. Relevant equations

3. The attempt at a solution

See my attached working

the answer is $u(x,y)=5ye^{y-1+x^{2}-x}$

Im not sure if Im getting anywhere near close in my working out. Have double checked the arithemetic and everything seems fine so far
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

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• ###### q50bp3.pdf
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2. Oct 25, 2011

### JamesGoh

hi guys

an update on the problem. I managed to solve it.

The issue was that I didn't consider the arbirtrary integration constant, C, when doing the integral of the Y term.