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b The differential equation y + 2y³ = (y² + 5x) y' can be written in differential form: where M(x, y) = M(x, y) dx + N(x, y) dy = 0 and N(x, y) = The term M(x,y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by yº. Integrating that new equation, the solution the differential equation is

b The differential equation y + 2y³ = (y² + 5x) y' can be written in differential form: where M(x, y) = M(x, y) dx + N(x, y) dy = 0 and N(x, y) = The term M(x,y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by yº. Integrating that new equation, the solution the differential equation is

Advanced Engineering Mathematics
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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b The differential equation y + 2y³ = (y² + 5x) y' can be written in differential form: where M(x, y) = M(x, y) dx + N(x, y) dy = 0 and N(x, y) = The term M(x,y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by yº. Integrating that new equation, the solution of the differential equation is = C.
Transcribed Image Text:b The differential equation y + 2y³ = (y² + 5x) y' can be written in differential form: where M(x, y) = M(x, y) dx + N(x, y) dy = 0 and N(x, y) = The term M(x,y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by yº. Integrating that new equation, the solution of the differential equation is = C.
a 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) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation (-1e* sin(y) - 2y)dx + (−2x − leª cos(y))dy = 0 First, if this equation has the form M(x, y)dx + N(x, y)dy = 0: My(x, y) and N₂(x, y) = = If the equation is not exact, enter not exact, otherwise enter in F(x, y) here
Transcribed Image Text:a 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) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation (-1e* sin(y) - 2y)dx + (−2x − leª cos(y))dy = 0 First, if this equation has the form M(x, y)dx + N(x, y)dy = 0: My(x, y) and N₂(x, y) = = If the equation is not exact, enter not exact, otherwise enter in F(x, y) here
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