Homework Help: Find the constants for given IVP

Feodalherren · Feb 7, 2015

1. The problem statement, all variables and given/known data

2. Relevant equations
DifEqs

3. 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 · Feb 7, 2015

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

Feodalherren · Feb 7, 2015

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

Svein · Feb 7, 2015

Feodalherren said: ↑

What am I doing wrong?

[itex] y=c_{1}e^{-4x}cos(x)+c_{2}e^{-4x}sin(x)[/itex]

[itex]y'=c_{1}(-4e^{-4x}cos(x)-e^{-4x}sin(x))+c_{2}(-4e^{-4x}sin(x)+e^{-4x}cos(x)) [/itex]

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

HallsofIvy · Feb 7, 2015

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

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

Feodalherren · Feb 7, 2015

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

Thanks