In we saw that cos x and e" were solutions of the nonlinear equation (y")2 -y2 = 0
Chapter 3, Problem 18(choose chapter or problem)
In we saw that cos x and e" were solutions of the nonlinear equation (y")2 -y2 = 0. Verify that sin x and e-x are also solutions. Without attempting to solve the differential equation, discuss how these explicit solutions can be found by using knowledge about linear equations. Without attempting to verify, discuss why the linear combinations y = c1e" + c 2 e-x + c3 cosx + c4 sinx andy = c2 e-x + c4 sinx are not, in general, solutions, but the two special linear combinations y = c1 e" + c 2 e-x and y = c3 cos x + c4 sin x must satisfy the differential equation.
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