MAT244-2013S > Term Test 1

TT1--Problem 2

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Victor Ivrii:
(a) Consider equation
\begin{equation*}
(\cos(t)+t\sin(t))y''-t\cos(t)y'+y\cos(t)=0.
\end{equation*}
Find wronskian $W=W[y_1,y_2](t)$ of two solutions such that $W(0)=1$.

(b) Check that  one of the solutions is $y_1(t)=t$. Find another solution $y_2$ such that $W[y_1,y_2](\pi/2)=\pi/2$
and $y_2(\pi/2)=0$.

Jeong Yeon Yook:
part a)

Jeong Yeon Yook:
Part (b).

Can I please get bonus marks?  :'( I couldn't do it under limited time and exam pressure. I don't know how how I couldn't see things in the exam center room.  Now things work out....

Marcia Bianchi:
part a)

Victor Ivrii:
See my comments to Problem 1. Waiting for typed solution.

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