Question

How can i find the general solution to the ordinary differential equation:
Y''(x) + Y'(x) - 2Y(x) = 0
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Answer 1

This second order differential equation with constant coefficients. It has solutions of the form e^mx. The auxiliary equation is given by:
\[m^2+m-2=0 \implies (m+2)(m-1)=0 \implies m=-2, m=1\]
Therefore, the general solution is:
\[y(x)=c_1e^{-2x}+c_2e^x\]

Answer 2

nice one thanks, i have seen that auxiliary equation before, when am i allowed to use it? What classification of equation?