System of Partial Differential Equations: Solving for u(x,y)

[menco]

Homework Statement

Solve the following system of partial differential equations for u(x,y)

Homework Equations

$$du/dy = 2xyu$$

$$du/dx = (y^2 + 5)u$$

The Attempt at a Solution

I am honestly not sure where to start, my lectures and tutorials this week have not been helpful at all. My guess is to take the derivative of the first equation and sub that into the second equation for y and then take the derivative of the second equation to get my final answer. But I am probably completely wrong. Any help or advice would be appreciated!

 

[ehild]

You can show that d(ln(u))=(y²+5)dx+2xy dy is an exact differential.

ehild

 

[ehild]

Homework Statement

Solve the following system of partial differential equations for u(x,y)

Homework Equations

$$du/dy = 2xyu$$

$$du/dx = (y^2 + 5)u$$

The Attempt at a Solution

Try to integrate both equations keeping the other variable as parameter, and include it also into the integration constant. You get the solutions in the form u(xy)=F(x,y) +f(x), u(xy)=G(x,y)+g(x). The two functions must be identical: you find the relation between f and g from this requirement.

ehild