Solving Second Order Differential Equations with Initial Value Problem

[rbailey5]

Homework Statement

I have got the diff equ problem solved out to

y(t)=Ce^-t*cos4t+Ce^-t*sin4t

Homework Equations

now I have to solve for the IVP and the values are y(0)=1, yprime(0)=-1

The Attempt at a Solution

I believe for the first part I just plug in the y(0)=1 which results in the e^-t dropping out
coming out to be C=1 but I am not 100% on it.

Then I am assuming I take the derivative and solve for the next value.

 

[SammyS]

Are you sure those shouldn't be two different constants, as in y(t) = C₁ e^-t cos(4t) + C₂ e^-t sin(4t)

Then, you found that C₁ = 1.

Now find y'(x) , then set y'(0) = -1 & solve for C₂ .