Show that the solution of the initial value problem L[ y
Question and Solution
Show that the solution of the initial value problem L[ y] = y?? + p(t)y? + q(t)y = g(t), y(t0) = y0, y? (t0) = y1 can be
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Show that the solution of the initial value problem L[ y] = y?? + p(t)y? + q(t)y = g(t), y(t0) = y0, y? (t0) = y1 can be written as y = u(t) + ?(t), where u and ? are solutions of the two initial value problems L[u] = 0, u(t0) = y0, u? (t0) = y1, L[?] = g(t), ?(t0) = 0, ?? (t0) = 0, respectively. In other words, the nonhomogeneities in the differential equation and in the initial conditions can be dealt with separately. Observe that u is easy to find if a fundamental set of solutions of L[u] = 0 is known
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