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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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.4: Total Differentials And Approximations
Problem 10E: Use the total differential to approximate each quantity. Then use a calculator to approximate the...
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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.
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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