Use the "mixed partials" check to see if the following differential equation is exact. f it is exact find a function F(x, y) whose differential, dF(x, y) gives the differential equation. That is, level curves F(x, y) = C are solutions to the diff equation: First rewrite as where M(x, y) and N(x, y) = -2x+2y^3 = -4x^4+2y dy dx = -4x+2y -2x + 2y³ M(x,y) dx + N(x, y) dy = 0
Use the "mixed partials" check to see if the following differential equation is exact. f it is exact find a function F(x, y) whose differential, dF(x, y) gives the differential equation. That is, level curves F(x, y) = C are solutions to the diff equation: First rewrite as where M(x, y) and N(x, y) = -2x+2y^3 = -4x^4+2y dy dx = -4x+2y -2x + 2y³ M(x,y) dx + N(x, y) dy = 0
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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Transcribed Image Text:Use
the "mixed partials" check to see if the following differential equation is exact.
If it is exact find a function F(x, y) whose differential, dF(x, y) gives the differential equation. That is, level curves F(x, y) = C are solutions to the differential
equation:
First rewrite as
where M(x, y) = -4x^4+2y
and N (x, y)
= -2x+2y^3
dy
dx
- 4x + 2y
-2x + 2y³
M(x, y) dx + N (x, y) dy = 0
If the equation is not exact, enter not exact, otherwise enter in F(x, y) as the solution of the differential equation here
-2xy+(y^4)/2+(4x^5)/5
= C.
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