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2. (a) Prove that the substitution u = y¹-n reduces the Bernoulli's equation dy + 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 dx x2 - 2xy = 3y³, y(1) = 1.

2. (a) Prove that the substitution u = y¹-n reduces the Bernoulli's equation dy + 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 dx x2 - 2xy = 3y³, y(1) = 1.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 15CR
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2. (a) Prove that the substitution u = y¹-n reduces the Bernoulli's equation dy ·+ 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 dx x². - 2xy = 3y³, === y(1) = 1.
Transcribed Image Text:2. (a) Prove that the substitution u = y¹-n reduces the Bernoulli's equation dy ·+ 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 dx x². - 2xy = 3y³, === y(1) = 1.
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