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2(a) Given that f(x, y) = 6x²y3 – cosx + 5y – siny + 10x, establish the fact that, the order in which the second order mixed partials derivatives are taken is immaterial. (b) Solve the separable differential equation 7е-3х + 2x2- хcosx -6y3 (c) Solve the IVP x(1 — siny)dy %3D (сosx — сosy — у)ӑх. x) = 0

2(a) Given that f(x, y) = 6x²y3 – cosx + 5y – siny + 10x, establish the fact that, the order in which the second order mixed partials derivatives are taken is immaterial. (b) Solve the separable differential equation 7е-3х + 2x2- хcosx -6y3 (c) Solve the IVP x(1 — siny)dy %3D (сosx — сosy — у)ӑх. x) = 0

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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2(a) Given that f(x, y) = 6x²y3 – cosx + 5y – siny + 10x, establish the fact that, the order in which the second order mixed partials derivatives are taken is immaterial. (b) Solve the separable differential equation 7е-3х + 2х2- хcosx -6y3 (c) Solve the IVP x(1 — siny)dy %3D (сosx — сosy — у)ӑх. x) = 0
Transcribed Image Text:2(a) Given that f(x, y) = 6x²y3 – cosx + 5y – siny + 10x, establish the fact that, the order in which the second order mixed partials derivatives are taken is immaterial. (b) Solve the separable differential equation 7е-3х + 2х2- хcosx -6y3 (c) Solve the IVP x(1 — siny)dy %3D (сosx — сosy — у)ӑх. x) = 0
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