Let y1 and y2 be solutions of a second order homogeneous linear differential equation y''+ p(x) y' + q(x) y = 0 , in R. Suppose that y1(x) + y2(x) = e-x , W [ y1(x) , y2(x) ] = ex , where W [ y1 , y2 ] is the Wronskian of y1 and y2 .a) Find p (x)b) Find q (x)c) Find the general form of y1 and y2 .

p(X)= -1 q(X) = -2 Y(X)= c1e2x+c2e-x

Answered: Let y1 and y2 be solutions of a second…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let y₁ and y₂ be solutions of a second order homogeneous linear differential equation y^''+ p(x) y^' + q(x) y = 0 , in R. Suppose that y₁(x) + y₂(x) = e^-x ,

W [ y₁(x) , y₂(x) ] = e^x , where W [ y₁ , y₂ ] is the Wronskian of y₁ and y₂ .

a) Find p (x)

b) Find q (x)

c) Find the general form of y₁ and y₂ .

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