dy If y,,y, are two solutions of the differentialequation +P(x),y%3DQ(x), dx Thenprove that y = y, +C(y, - y2)is the general solution of the equation where Cis an arbitrary constant.For what relation between the constant a, b will the linear combination a y, +by, also be a solution?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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dy
If y,,y2 are two solutions of the differential equation +P(x),y=Q(x),
dx
Then prove that y = y, +C(y, - Y2)is the general solution of the equation where
Cis an arbitrary constant.For whatrelation between the constant a, b will the
linear combinationay, +by, alsobe a solution?
Transcribed Image Text:dy If y,,y2 are two solutions of the differential equation +P(x),y=Q(x), dx Then prove that y = y, +C(y, - Y2)is the general solution of the equation where Cis an arbitrary constant.For whatrelation between the constant a, b will the linear combinationay, +by, alsobe a solution?
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