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If ##y_1## and ##y_2## are homogenous solutions to a (not necessarily homogenous) second order linear ODE, we define the Wronskian as $$\begin{vmatrix}

y_1 y_2\\

y'_1 y'_2

\end{vmatrix}$$. This derivation seems to stem from the pair of equations involving ##y_1## and ##y_2## satisfying the initial conditions ##y(t_0) = y_0## and ##y'(t_0) = y'_0##. But we never satisfy the initial conditions with only ##y_1## and ##y_2## until we also have the particular solution. If everything I've said so far is correct, why is the Wronskian defined in this manner?

Thanks so much!

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# Wronskian question

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