Question

The solution of a certain differential equation is of the form y(t) = a exp(2 t) + b exp(5 t), where a and b are constants. The solution has initial conditions y(0) = 3 and y'(0) = 5 . Find the solution by using the initial conditions to get linear equations for a and b.

Answer 1

so the given solution is\[y(t)=Ae^{2t}+Be^{5t}\]and you want to find A and B given the initial conditions?

Answer 2

...correct?

Answer 3

Yes :)

Answer 4

what is y'(t) ?

Answer 5

..and sorry for the late reply

Answer 6

find y'(t)
the plug t=0 into each equation
y(0)=3
y'(0)=5

this will give you a linear system of two equations that can be solved for A and B

Answer 7

Can you tell me what you get for the linear system, I don't think I did it right :/