a) Verify that when changing the variable u = ln (y) the equation (see img 1) becomes a Bernoulli equation. (b) Find the general solution to the equation. (c) Find the particular solution subject to the initial condition y (0) = e. Hint: The equality (see img 2) may be helpful.

a) Verify that when changing the variable u = ln (y) the equation (see img 1) becomes a Bernoulli equation. (b) Find the general solution to the equation. (c) Find the particular solution subject to the initial condition y (0) = e. Hint: The equality (see img 2) may be helpful.

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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Question

(a) Verify that when changing the variable u = ln (y) the equation

(see img 1)

becomes a Bernoulli equation.

(b) Find the general solution to the equation.

Hint: The equality (see img 2) may be helpful.

S arctan(x)dx = x arctan(x)
In(r² +1)
+C
2

(In(y))³y' – arctan(x)(ln(y))*y= xe4z arctan(2) y.

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