Suppose that y1(t) and y2(t) are both solutions to the differential equation
dy/dt= a(t)y + b(t).
Write down a linear differential equation satisfied by y1(t) + y2(t).

Question

Suppose that y1(t) and y2(t) are both solutions to the differential equation
dy/dt= a(t)y + b(t).
Write down a linear differential equation satisfied by y1(t) + y2(t).

bahrom7893 · Answer

crap i forgot how to do this lol.. hold on... let's roll those marbles around

bahrom7893 · Answer

Turing do u remember how to do this?

turingtest · Answer

I'm not sure if you need to actually solve it or not...

bahrom7893 · Answer

No you don't.. I don't think so.. It's like this form with the constant

jamesj · Answer

If y1 and y2 are solutions to that above equation, then for each of them
y' - a(t)y = b(t)

Hence 
y1' - a(t)y1 = b(t)
y2' - a(t)y2 = b(t)

Add these equations together and you'll see what is the linear INhomogeneous equation satisfied by y1 + y2

bahrom7893 · Answer

OHHHHH JamesJ tnx lol

jamesj · Answer

I guess the point of this exercise is to show you that the sum of solutions to an inhomogeneous equation cannot be added together, as would be the case with solutions to a homogeneous equation.

turingtest · Answer

ahhh...