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Test Yourself 02 dy UTransform the following Bernoulli differential equation of the form + P(x) · y = dx Q(x)y" or dy + P(y) : = Q(y) · x" into a linear form using a corresponding substituting variable u. du 1 1) 2хуу' %3D у? — 2х3 Ans: -и %3 - 2х2 (Хіе, 2010) dx du 1 2) 3ydx – x(3x³y ln y + 1)dy = 0 Ans: dy u = -3 In y (Xie, 2010) y dy 3) 2- y = xy5 Ans: du + 4· u = -4x (Ayres, Differential Equations, 1952) dx dx dy du 4) dx + 2xy + xy* = 0 Ans: dx 6x · u = 3x (Ayres, Differential Equations, 1952)

Test Yourself 02 dy UTransform the following Bernoulli differential equation of the form + P(x) · y = dx Q(x)y" or dy + P(y) : = Q(y) · x" into a linear form using a corresponding substituting variable u. du 1 1) 2хуу' %3D у? — 2х3 Ans: -и %3 - 2х2 (Хіе, 2010) dx du 1 2) 3ydx – x(3x³y ln y + 1)dy = 0 Ans: dy u = -3 In y (Xie, 2010) y dy 3) 2- y = xy5 Ans: du + 4· u = -4x (Ayres, Differential Equations, 1952) dx dx dy du 4) dx + 2xy + xy* = 0 Ans: dx 6x · u = 3x (Ayres, Differential Equations, 1952)

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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Test Yourself 02 dy UTransform the following Bernoulli differential equation of the form 2+ P(x) · y = dx dx Q(x)y" or dy + P(y) : = Q(y) · x" into a linear form using a corresponding substituting variable u. du 1 1) 2хуу' %3D у? — 2х3 Ans: -и %3 - 2х2 (Хіе, 2010) II dx du 1 2) 3ydx – x(3x³y ln y + 1)dy = 0 Ans: dy u = -3 In y (Xie, 2010) y dy 3) - y = xy5 Ans: du + 4· u = -4x (Ayres, Differential Equations, 1952) dx dx dy + 2xy + xy* 4) dx du = 0 Ans: dx 6x · u = 3x (Ayres, Differential Equations, 1952)
Transcribed Image Text:Test Yourself 02 dy UTransform the following Bernoulli differential equation of the form 2+ P(x) · y = dx dx Q(x)y" or dy + P(y) : = Q(y) · x" into a linear form using a corresponding substituting variable u. du 1 1) 2хуу' %3D у? — 2х3 Ans: -и %3 - 2х2 (Хіе, 2010) II dx du 1 2) 3ydx – x(3x³y ln y + 1)dy = 0 Ans: dy u = -3 In y (Xie, 2010) y dy 3) - y = xy5 Ans: du + 4· u = -4x (Ayres, Differential Equations, 1952) dx dx dy + 2xy + xy* 4) dx du = 0 Ans: dx 6x · u = 3x (Ayres, Differential Equations, 1952)
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