Thread: verify that the pair of functions is a solution...

verify that the pair of functions x = t + e^t , y = te^t is a solution to the system of differential equations.

x + y - dy/dt = 1 , x - dx/dt = t - 1.

ok so i was able to prove that the pair of functions were solutions to the x + y - dy/dt = 1.

but i couldnt prove they were solutions to the equation on the right, x - dx/dt = t - 1.

any thoughts? thanks in advance.

to do this problem i substituted the two equations into the x + y - dy/dt = 1. and solved it for dy/dt, the problem checked out. but i couldnt do that with the other side?? any thoughts?

, so .

What does equal?

sorry, X - dx/dt = t - 1

Exactly...

.


Therefore we have verified is a solution to that DE.

ok but what about the function with the y in it? wouldnt i have to prove that y=te^t is also a solution of x-dx/dt = t-1 ?

How can it be? There's no in it...

thats what i was hoping. my prof wanted me to prove that both were solutions. thank you!

Originally Posted by slapmaxwell1

thats what i was hoping. my prof wanted me to prove that both were solutions. thank you!

What I mean is, in the second DE can be anything, as the DE doesn't depend on it.

So to have a solution to both DEs, you just need a that satisfies the first...