Linear equation:
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The terms linear in y are the homogeneous part, the terms independent of y are the inhomogeneous term.
Linear equations allow solutions to be added:

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Solve the homogeneous equation first:
y' + p y = 0
Separable:![]()
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Now solve the inhomogeneous equation:
Variation of parameter:
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Put in the O.D.E. and solve for C(x).