ATAR Notes: Forum

Uni Stuff => Science => Faculties => Mathematics => Topic started by: /0 on February 22, 2010, 12:05:59 am

Title: A DE
Post by: /0 on February 22, 2010, 12:05:59 am: NVM IGNORE THIS ONE :D
*FACEPALM*&

$\dot{y}+0.1y = 0.1e^{-0.1t}$

When trying to find the particular solution, I chose $y_p = Ae^{-0.1t}$

$\dot{y}_p = -0.1Ae^{-0.1t}$

What happens when

$-0.1Ae^{-0.1t}+0.1Ae^{-0.1t}=0.1e^{-0.1t}$

$e^{-0.1t}=0$ ?

thx xD
Title: Re: A DE
Post by: Ahmad on February 22, 2010, 12:08:10 am: $y = Ae^{-0.1t}$ is a solution to the homogeneous equation, which means you should alter your ansatz to t multiplied by your initial guess, so $y_p = At\cdot e^{-0.1t}$ .