Solve step by step in digital formatSolve the exact differential equation(2x + 4) dx + (3y - 1) dy = 0answer x² + 4x + y² - y = c

A differential equation of the form is said to be exact if the left hand member is the exact…

Answered: Solve step by step in digital format…

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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Solve step by step in digital format
Solve the exact differential equation
(2x + 4) dx + (3y - 1) dy = 0
answer x² + 4x + y² - y = c

Expert Solution

Step 1: Definition of Exact differential equation

A differential equation of the form $M left parenthesis x comma y right parenthesis d x space plus space N left parenthesis x comma y right parenthesis d y equals 0$ is said to be exact if the left hand member is the exact differential of some function $f left parenthesis x comma y right parenthesis$ i.e. $d f equals M d x plus N d y$ .

Theorem : The necessary and sufficient condition for a differential equation $M d x space plus space N d y space equals space 0$ to be exact is

$fraction numerator partial differential M over denominator partial differential y end fraction equals fraction numerator partial differential N over denominator partial differential x end fraction$