(a) Prove that the substitution ? = ?1−? reduces the Bernoulli’s equation????+ ?(?)? = ?(?)??, ? ≠ 0 , ? ≠ 1to a linear equation in ?.(b) Find the solution of the nonlinear IVP?2 ????− 2?? = 3?3, ?(1) = 1. 2. (a) Prove that the substitution u = yl¬n reduces the Bemoulli's equation1-n+ P(x)y = f(x)y", n ± 0 , n ± 1dxto a linear equation in u.(b) Find the solution of the nonlinear IVPdyx2- 2xydx3y³,y(1) = 1.

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Answered: 2. (a) Prove that the substitution u =…

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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(a) Prove that the substitution ? = ?1−? reduces the Bernoulli’s equation
??
??
+ ?(?)? = ?(?)??, ? ≠ 0 , ? ≠ 1
to a linear equation in ?.
(b) Find the solution of the nonlinear IVP
?2 ??
??
− 2?? = 3?3, ?(1) = 1.

2. (a) Prove that the substitution u = yl¬n reduces the Bemoulli's equation
1-n
+ P(x)y = f(x)y", n ± 0 , n ± 1
dx
to a linear equation in u.
(b) Find the solution of the nonlinear IVP
dy
x2
- 2xy
dx
3y³,
y(1) = 1.

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