Solved: Reduce to first order and solve (showing each step
Chapter 2, Problem 2.1.22(choose chapter or problem)
REDUCTION OF ORDER is important because it gives a simpler ODE. A second-order ODE F(x, y, y’, y’’) = 0, linear or not, can be reduced to first order if y does not occur explicitly (Prob. 15) or if x does not occur explicitly (Prob. 16) or if the ODE is homogeneous linear and we know a solution (see the text).
(Reduction) Show that F(x,y’,y’’) = 0 can be reduced to first order in z = y’ from which y follows by integration). Give two examples of your own.
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