Find the constants for given IVP

[Feodalherren]

Homework Statement

Homework Equations

DifEqs

The Attempt at a Solution

y ' = 4C₁e^-4xSinX - 4C₂e^-4xCosX

y'(0) = -1

-1 = 0 - 4C₂

Therefore

C₂ = 1/4

Not correct. What am I doing wrong?

 

[vela]

You didn't differentiate correctly. You have to use the product rule.

 

[Feodalherren]

Sigh... obviously. Can't believe I just did that. Thanks!

 

[Svein]

What am I doing wrong?

1. y=c_{1}e^{-4x}cos(x)+c_{2}e^{-4x}sin(x)
2. y'=c_{1}(-4e^{-4x}cos(x)-e^{-4x}sin(x))+c_{2}(-4e^{-4x}sin(x)+e^{-4x}cos(x))

Now insert for y(0) and y'(0) and solve.

 

[HallsofIvy]

Personally, I would find it easier to write the solution as y= e^{-4x}(C_1 cos(x)+ C_2 sin(x)).

Then, by the product rule, y'= -4e^{-4x}(C_1 cos(x)+ C_2 sin(x))+ e^{-4x}(-C_1 sin(x)+ C_2 cos(x)).

 

[Feodalherren]

Yeah I got it dudes. I was just being stupid and completely forgot the product rule.

Thanks