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(a) For x > 0, consider the homogeneous ordinary differential equation 1 „2 dy dx (2² + y³) for the dependent variable y. (i) Introduce a new dependent variable z by and transform this homogeneous equation into a separable one for z. (ii) Obtain the general solution of this separable equation in the form G(r, z) = C for some function G and arbitrary constant C.

(a) For x > 0, consider the homogeneous ordinary differential equation 1 „2 dy dx (2² + y³) for the dependent variable y. (i) Introduce a new dependent variable z by and transform this homogeneous equation into a separable one for z. (ii) Obtain the general solution of this separable equation in the form G(r, z) = C for some function G and arbitrary constant C.

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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Question 1 (a) For x > 0, consider the homogeneous ordinary differential equation dy 1 2 (x² + y²) 2 dx for the dependent variable y. (i) Introduce a new dependent variable z by Y 2 = and transform this homogeneous equation into a separable one for z. (ii) Obtain the general solution of this separable equation in the form G(x, z) = C for some function G and arbitrary constant C.
Transcribed Image Text:Question 1 (a) For x > 0, consider the homogeneous ordinary differential equation dy 1 2 (x² + y²) 2 dx for the dependent variable y. (i) Introduce a new dependent variable z by Y 2 = and transform this homogeneous equation into a separable one for z. (ii) Obtain the general solution of this separable equation in the form G(x, z) = C for some function G and arbitrary constant C.
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