Answered: 26. xy" + y' = x

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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The instructions say: "It is possible to solve a second-order differential equation of the form y" = F(x, y′) by letting v = y′,
v′ = y″ and arriving at a first-order equation of the form v′ = F(x, v). If this new equation in v can
be solved, it is then possible to find y by integrating dy/dx = v(x). Note that a constant will be
obtained in solving the first-order equation in v, and another constant will be obtained in
integrating dy/dx. Solve the given differential equations with missing y."

I try doing this but am unsure how to get to the solution that the textbook has, as I keep getting a drastically different answer.

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