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Transform the following Bernoulli differential equation of the form 2+ P(x) · y = dx Q(x)y" or + P(y) · x = Q(y) - x" into a linear form using a corresponding dy substituting variable u. 1 1) 2xyy' = y2 – 2x³ Ans: du u = -2x² (Xie, 2010) -- %3D dx

Transform the following Bernoulli differential equation of the form 2+ P(x) · y = dx Q(x)y" or + P(y) · x = Q(y) - x" into a linear form using a corresponding dy substituting variable u. 1 1) 2xyy' = y2 – 2x³ Ans: du u = -2x² (Xie, 2010) -- %3D dx

Advanced Engineering Mathematics
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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Transform the following Bernoulli differential equation of the form 2 + P(x) · y = dx Q(x)y" or + P(y) · x = Q(y) · x" into a linear form using a corresponding dy substituting variable u. du 1 1) 2xyy' = y2 – 2x³ Ans: dx u = -2x² (Xie, 2010) 2) 3ydx – x(3x³y ln y + 1)dy = 0 Ans: dy +u = -3 In y (Xie, 2010) y dy du 3) 2- y = xys Ans: + 4.u = -4x (Ayres, Differential Equations, 1952) dx du 4) 2+ 2xy + xy* = 0 Ans: – 6x · u = 3x (Ayres, Differential Equations, 1952) dx
Transcribed Image Text:Transform the following Bernoulli differential equation of the form 2 + P(x) · y = dx Q(x)y" or + P(y) · x = Q(y) · x" into a linear form using a corresponding dy substituting variable u. du 1 1) 2xyy' = y2 – 2x³ Ans: dx u = -2x² (Xie, 2010) 2) 3ydx – x(3x³y ln y + 1)dy = 0 Ans: dy +u = -3 In y (Xie, 2010) y dy du 3) 2- y = xys Ans: + 4.u = -4x (Ayres, Differential Equations, 1952) dx du 4) 2+ 2xy + xy* = 0 Ans: – 6x · u = 3x (Ayres, Differential Equations, 1952) dx
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