Example 13.15.15. [P and Q are functions of x and y. Then Pdx + Qdy is called aperfect differential or exact differential of some function z of x and y if dz = Pdx+Qdy).1. If Pdr + Qdy be a perfect diffcrential of some function z of x and y, then provethat2. If Pdx + Qdy + Rdz can be made a perfect differential of some function of x, y, zby multiplying each term by a common factor µ(1. y, z), then prove thataR+ QPdz+ RD0.|dzду

Example 13.15.15. [P and Q are functions of x and y. Then Pdx + Qdy is called a perfect differential or exact differential of some function z of x and y if dz = Pdr+Qdy]. %3D 1. If Pdx + Qdy be a perfect differential of some function z of r and y, then prove ӘР that dy %3D 2. If Pdx + Qdy + Rdz can be made a perfect differential of some function of x, y, z by multiplying each term by a common factor µ(I. y, z), then prove that aR +Q az OP + R dz = 0. Əx ) dy

Example 13.15.15. [P and Q are functions of x and y. Then Pdx + Qdy is called a perfect differential or exact differential of some function z of x and y if dz = Pdr+Qdy]. %3D 1. If Pdx + Qdy be a perfect differential of some function z of r and y, then prove ӘР that dy %3D 2. If Pdx + Qdy + Rdz can be made a perfect differential of some function of x, y, z by multiplying each term by a common factor µ(I. y, z), then prove that aR +Q az OP + R dz = 0. Əx ) dy

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Example 13.15.15. [P and Q are functions of x and y. Then Pdx + Qdy is called a
perfect differential or exact differential of some function z of x and y if dz = Pdx+Qdy).
1. If Pdr + Qdy be a perfect diffcrential of some function z of x and y, then prove
that
2. If Pdx + Qdy + Rdz can be made a perfect differential of some function of x, y, z
by multiplying each term by a common factor µ(1. y, z), then prove that
aR
+ Q
P
dz
+ R
D0.
|
dz
ду

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