- #1

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- Homework Statement
- u_x + x*u_y = (y-1/2x^2)^2, u(0,y) = e^y

- Relevant Equations
- du/dt = du/dx*dx/dt + du/dy*dy/dt

dx/dt =1, x(0,s)=0, dy/dt=x, y(0,s) = s, du/dt=(y-1/2x^2)^2, u(0,s)=e^s

I did well at the beginning to get x(t,s) =t and y(t,s)=1/2t^2 + s, but got stuck with the du/dt part.

You can sub in x=t and y=1/2t^2 +s for x and y to get du/dt = s^2. But that's still three variables, and I can't see any obvious substitutions.

This is a regular diffy Q course, so I don't have a lot of knowledge of advanced techniques, and this was just thrown in, so I'm a little unsure how to proceed.

I did well at the beginning to get x(t,s) =t and y(t,s)=1/2t^2 + s, but got stuck with the du/dt part.

You can sub in x=t and y=1/2t^2 +s for x and y to get du/dt = s^2. But that's still three variables, and I can't see any obvious substitutions.

This is a regular diffy Q course, so I don't have a lot of knowledge of advanced techniques, and this was just thrown in, so I'm a little unsure how to proceed.