Solve the differential equation (2x³ - 8xy³ – 18x) dx + (12x²y² + 3y³ − 6y²) dy = 0 - using the following steps. (i) Show that by applying the substitution u = x², v = y³, the differential equation becomes M(u, v) du + N(u, v) dv = 0, where M and N are linear functions of u and v. (ii) Find the unique solution (uo, vo) of the linear system of equations M(u, v) N(u, v) = 0. Afterwards, apply another substitution r = u — uo, s = v-vo. The new differential equation in r and s is now homogeneous and can be solved using the method you learned in class. = 0
Solve the differential equation (2x³ - 8xy³ – 18x) dx + (12x²y² + 3y³ − 6y²) dy = 0 - using the following steps. (i) Show that by applying the substitution u = x², v = y³, the differential equation becomes M(u, v) du + N(u, v) dv = 0, where M and N are linear functions of u and v. (ii) Find the unique solution (uo, vo) of the linear system of equations M(u, v) N(u, v) = 0. Afterwards, apply another substitution r = u — uo, s = v-vo. The new differential equation in r and s is now homogeneous and can be solved using the method you learned in class. = 0
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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Transcribed Image Text:Solve the differential equation
(2x³ - 8xy³ – 18x) dx + (12x²y² + 3y³ − 6y²) dy = 0
-
using the following steps.
(i) Show that by applying the substitution u = x², v = y³, the differential equation becomes
M(u, v) du + N(u, v) dv = 0,
where M and N are linear functions of u and v.
(ii) Find the unique solution (uo, vo) of the linear system of equations
M(u, v)
N(u, v) = 0.
Afterwards, apply another substitution r = u — uo, s = v-vo. The new differential equation
in r and s is now homogeneous and can be solved using the method you learned in class.
= 0
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