Help me fast so that I will give good rating..... a) (x2 — у?)dx + 2хydy %3D 0b) (у+ху?)dx + (x — х?у)dy %3D 0PyI) A = 1(x)Qxa(x)= ePy – QxII) A = A(y) ·—РPy – Qx( — РPy – Qx– QxIII) 2 = 1(xy)IV) A = 1(x+y) →V) 2 = 1(x – y) →Q + PyQ – xPVI) A = A(x² + y²)Py - Qx2xQ — 2уР"VII) λ (x2-y)Py – Qx2x0 + 2уР

We have to solve given problems:

а) (x2 — у?)dx + 2хydy %3D 0 b) (у+ ху?)dx + (х— х?у)dy %3D 0 Py – Qx Py – Qx I) A = 1(x) → 1(x) )λ = λ) = e —Р By – Qx Py – Qx I)λ= A( +y) - Py – Qx III) A = A(xy) Όλ = λ( -) - Q + P yQ – xP * Q - P' Py – Qx 2xQ — 2уР" Py – Qx 2xQ + 2уP VI) 1 = 1(x² + y²) VI) λ λ(x?- y ) -

а) (x2 — у?)dx + 2хydy %3D 0 b) (у+ ху?)dx + (х— х?у)dy %3D 0 Py – Qx Py – Qx I) A = 1(x) → 1(x) )λ = λ) = e —Р By – Qx Py – Qx I)λ= A( +y) - Py – Qx III) A = A(xy) Όλ = λ( -) - Q + P yQ – xP * Q - P' Py – Qx 2xQ — 2уР" Py – Qx 2xQ + 2уP VI) 1 = 1(x² + y²) VI) λ λ(x?- y ) -

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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Help me fast so that I will give good rating.....

a) (x2 — у?)dx + 2хydy %3D 0
b) (у+ху?)dx + (x — х?у)dy %3D 0
Py
I) A = 1(x)
Qx
a(x)
= e
Py – Qx
II) A = A(y) ·
—Р
Py – Qx
( — Р
Py – Qx
– Qx
III) 2 = 1(xy)
IV) A = 1(x+y) →
V) 2 = 1(x – y) →
Q + P
yQ – xP
VI) A = A(x² + y²)
Py - Qx
2xQ — 2уР"
VII) λ (x2-y)
Py – Qx
2x0 + 2уР

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