Toronto Math Forum
MAT2442013S => MAT244 MathTests => MidTerm => Topic started by: Victor Ivrii on March 06, 2013, 09:06:36 PM

Find solution $y_2(t)$ of
\begin{equation*}
(t^21) y''2ty'+2 y=0
\end{equation*}
where one of the solutions is $y_1(t)=t$ and solution $y_2$ is such that $W(y_1,y_2)=1$ at $t=0$ and $y_2(0)=1$.

part 1

J. Yook' solution is correct. Note $\int \frac{2t}{t^21} \,dt = \ln (1t^2)+ \ln C$ as numerator is a derivative of denominator (no need to invoke partial fractions). It should be also noted that we are talking about interval $(1,1)$ as $t=\pm 1$ are breaking points (senior coefficient vanishes there) and $t=0$ selects this interval.