Differential equations assignment T6

[mathi85]

Hi!

I would like to ask anyone with some spare time to check my assignment questions. Last time I was asked to post one task at a time so I will.
Thank you in advance for your time.

Task 6:

In a galvanometer the deflection θ satisfies the diffrential equation:

d²θ/dt²+2(dθ/dt)+θ=4

Solve the equation for θ given that when t=0, θ=0 and dθ/dt=0


Solution:

d²θ/dt²+2(dθ/dt)+θ=4

m²+2m+1=0

m=-1

CF:
∴u=(At+B)e^-t

PI:
v=k
v'=0
v''=0

k+2(0)+0=4
k=4
∴v=4

GS:
θ=(At+B)e^-t+4

0=(A(0)+B)e⁰+4
0=B+4
B=-4

dθ/dt=(At-4)(-e^-t)+Ae^-t
0=(A(0)-4)(-e⁰)+Ae⁰
0=4+A
A=-4

PS:
θ=(-4t-4)e^-t+4

 

[jedishrfu]

Why don't you check them yourself and show what you did?

 

[mathi85]

I'm not sure if it's right but that's how I checked it:

θ=(At+B)e^-t+4
dθ/dt=(At+B)(-e^-t)+Ae^-t
d²θ/dt²=(At+B)(e^-t)+A(-e^-t)-Ae^-t

t=0
θ=0
dθ/dt=0
A=-4
B=-4

[d²θ/dt²=(At+B)(e^-t)+A(-e^-t)-Ae^-t]+2[0]+[(At+B)e^-t+4]=4

-4+4+4-4+4=4