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## Homework Statement

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

the given conditions

[itex]\frac{du}{dx}+y\frac{du}{dy}=(2x+y)u[/itex]

[itex]u(x,1)=5e^{x^{2}-x}[/itex]

## Homework Equations

## The Attempt at a Solution

See my attached working

the answer is [itex]u(x,y)=5ye^{y-1+x^{2}-x}[/itex]

Im not sure if Im getting anywhere near close in my working out. Have double checked the arithemetic and everything seems fine so far