Uncoupling Equations: A Matrix Approach

[Winzer]

Homework Statement

I am having trouble remembering how to uncouple these.

Homework Equations

$$\frac{dt}{ds}=1$$
$$\frac{du}{ds}=2tu$$

The Attempt at a Solution

I remember putting it into a matrix.
$$x'=\lambda x$$

 

[Mark44]

The equation with du/ds is nonlinear, so this system might not be amenable to uncoupling by matrix methods, which involves finding eigenvalues and eigenvectors, and using them to diagonalize a matrix.

Alternatively, I think it works to solve for t as a function of s in the first equation, and substitute for t in the second equation, and solve it for u.

To get you started, if dt/ds = 1, what is t as a function of s? Hint: there is not just one solution.

 

[Winzer]

t(s)=s+C

Plugging that into the latter u = A Exp(s^2+Cs). Is that right?

 

[HallsofIvy]

t(s)=s+C

Plugging that into the latter u = A Exp(s^2+Cs). Is that right?

Check it your self! Certainly dt/ds= 1. What is du/ds? Is it equal to 2tu?