Anyone good with differential equations ??

y'' + 4y' + 4y = et initial value y'(0)=2 , y(0)=1

Question

Anyone good with differential equations ??

y'' + 4y' + 4y = et  initial value y'(0)=2 , y(0)=1

anonymous · Answer

oh and ps its e^t

myininaya · Answer

first have you solve the for the homogeneous solution?

anonymous · Answer

no i havent tried i think they somehow use laplace transforms

myininaya · Answer

do we have to use laplace?

anonymous · Answer

no just solve as is so find characteristic equation and then sub in cuachy euler

anonymous · Answer

no just solve as is so find characteristic equation and then sub in cuachy euler

myininaya · Answer

i don't know this cuachy euler business

myininaya · Answer

i can show you how i would solve it

anonymous · Answer

okay

myininaya · Answer

r^2+4r+4=0
(r+2)^2=0
r=-2
so we have
$$y_h=c_1e^{-2t}+c_2te^{-2t}$$
now we need to find particular solution

myininaya · Answer

$$y_p=Ae^{t}=> y_p^{'}=Ae^{t}=>y_p^{''}=Ae^{t}$$
$$Ae^t+4Ae^t+4Ae^t=9Ae^t=e^{t}=>A=\frac{1}{9}$$

myininaya · Answer

$$y=y_h+y_p=c_1e^{-2t}+c_2te^{-2t}+\frac{1}{9}e^{t}$$

myininaya · Answer

myininaya · Answer

also you can apply the initial conditions right?