# Toronto Math Forum

## MAT244-2013S => MAT244 Math--Tests => Final Exam => Topic started by: Victor Ivrii on April 17, 2013, 03:02:14 PM

Title: FE-3
Post by: Victor Ivrii on April 17, 2013, 03:02:14 PM
\begin{equation*}
y^{(4)} -3y''-4y = \sin (t)+8 t.
\end{equation*}
Title: Re: FE-3
Post by: Jason Hamilton on April 17, 2013, 04:28:47 PM
solve homogeneous->  roots are i,-i,2,-2

Yh=c1 e^2t +c2 e^-2t +c3 cost +c4 sint

Yp-> undetermined coefficients-> Yp= Atcost +Btsint +Ct +D

evaulate polynomial terms => C=-2. D=0

evaulate sinusoidal terms => A=1/10 B=0

Y= c1 e^2t +c2 e^-2t +c3 cost +c4 sint + (1/10)tcost -2t
Title: Re: FE-3
Post by: Jason Hamilton on April 17, 2013, 04:31:38 PM
Also, I MIGHT have used 'x' instead of 't' on the test, would I lose marks if I used the wrong variable?
Title: Re: FE-3
Post by: Victor Lam on April 17, 2013, 06:14:16 PM
i did this
Title: Q3
Post by: Benny Ho on April 17, 2013, 09:17:02 PM
Solutions
Title: Re: FE-3
Post by: Victor Ivrii on April 17, 2013, 11:25:23 PM
Benny, WTH you posted Q1 into FE-3 and Q3 into FE-1 (so I needed to split and merge)?