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Quiz 2 \hfill  Show your work \break
Feb 19, 2016 \hfill  Circle your answer.

[10]~ 1.)  Given that $y(x) = x^{3 \over 2}$ and $y(x) = {1 \over x}$  are solutions to $2x^2y'' + xy' - 3y = 0$, state the general solution to this 2nd order homogeneous linear differential equation:

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%$2t^2(2t^{-3}) + t(-t^{-2}) - 3(t^{-1}) =4(t^{-1}) - t^{-1} - 3(t^{-1}) = 0$

%$2t^2({3 \over 4}t^{-1 \over 2}) + t({3 \over 2} t^{1 \over 2}) - 3( t^{3 \over 2}) =({3 \over 2}t^{3 \over 2}) + ({3 \over 2} t^{3 \over 2}) - 3( t^{3 \over 2})= 0$


%$t^2(6t) + t(3t^{2}) - 9(t^{3}) =4(t^{-1}) - t^{-1} - 3(t^{-1}) = 0$

%$t^2(2) + t(2t) - 4(t^{2}) =4(t^{-1}) - t^{-1} - 3(t^{-1}) = 0$


%Answer:$\underline{~~\hskip 2in~~}$


[10]~ 2.)  Solve: $y' = y~sin(x) + y$.

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%Answer:$\underline{~~\hskip 2in~~}$
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