# PDE separation of variable problem

## Homework Statement

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

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

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

## 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

## The Attempt at a Solution

#### Attachments

• q50bp1.pdf
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• q50bp2.pdf
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