- #1

gop

- 58

- 0

## Homework Statement

The temperature is given by

[tex]T(x,y)=\sqrt{2}e^{-y}\cos x[/tex]

Calculate the path of a heat-seeking particle.

## Homework Equations

## The Attempt at a Solution

[tex]\nabla f(x,y)=\left[\begin{array}{c}

-\sqrt{2}e^{-y}\sin x\\

-\sqrt{2}e^{-y}\cos x\end{array}\right][/tex]

[tex]g(t)=\left[\begin{array}{c}

g_{1}(t)\\

g_{2}(t)\end{array}\right][/tex]

[tex]\dot{g}_{1}(t)=-\sqrt{2}e^{-g_{2}(t)}\sin g_{1}(t)[/tex]

[tex]\dot{g}_{2}(t)=-\sqrt{2}e^{-g_{2}(t)}\cos g_{1}(t)[/tex]

That's where I'm stuck. I have to solve the differential equations but they depend very heavily on each other so I can't get them decoupled.

Also tried to solve them in maple but maple just complains that the numverator of the ODE depens on the highest derivative.

Do I missing something obvious? (we did differential equations only briefly)