ƏM ƏN ду дх exact differential equation, we multiply eq. 1 by 1 where ƏM ƏN dy¯əx N = f(x) then a= eS (x) dx

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.4: Solving Nonlinear Equations
Problem 17E: Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law,...
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Determination of Integrating Factor (Reduction to Exact
Differential Equation)
Considering the equation
M(x,y)dx + N(x, y) = 0 -------- eq.1
If,
ƏM
aN
dy " əx
To reduce eqn. 1 to an exact differential equation, we multiply eq. 1 by a where
a is an integrating factor.
Integrating Factors:
If
ƏM ƏN
dyəx
= f(x) then a = eS S(x) dx
If
aM
ƏN
ду
ax
M
g(y) then A= e-S9v) dy
Transcribed Image Text:Determination of Integrating Factor (Reduction to Exact Differential Equation) Considering the equation M(x,y)dx + N(x, y) = 0 -------- eq.1 If, ƏM aN dy " əx To reduce eqn. 1 to an exact differential equation, we multiply eq. 1 by a where a is an integrating factor. Integrating Factors: If ƏM ƏN dyəx = f(x) then a = eS S(x) dx If aM ƏN ду ax M g(y) then A= e-S9v) dy
Reduction to Exact Differential Equation
3
(x² + 3y2 + 6y)dy +-(x² + y²)dx = 0
Transcribed Image Text:Reduction to Exact Differential Equation 3 (x² + 3y2 + 6y)dy +-(x² + y²)dx = 0
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