(a) Show that yc.x/ D CeR P .x/ dx is a general solution
Chapter , Problem 31(choose chapter or problem)
(a) Show that yc.x/ D CeR P .x/ dx is a general solution of dy=dx C P .x/y D 0. (b) Show that yp.x/ D eR P .x/ dx Z Q.x/e R P .x/ dx dx is a particular solution of dy=dx C P .x/y D Q.x/. (c) Suppose that yc.x/ is any general solution of dy=dx C P .x/y D 0 and that yp.x/ is any particular solution of dy=dx C P .x/y D Q.x/. Show that y.x/ D yc.x/ C yp.x/ is a general solution of dy=dx C P .x/y D Q.x/. 32
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