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Solve the following DEs (in implicit form): (a) [x² + cos y ]dy + [2xy]dx = 0 dy (b) _xy − y² + (1 − xy) - 0 dx (c) (3x²y + 2xy + y³)dx + (x² + y²) dy = 0 =

Solve the following DEs (in implicit form): (a) [x² + cos y ]dy + [2xy]dx = 0 dy (b) _xy − y² + (1 − xy) - 0 dx (c) (3x²y + 2xy + y³)dx + (x² + y²) 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
Section9.2: Partial Derivatives
Problem 30E
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Solve the following DEs (in implicit form): (a) [x² + cos y ]dy + [2xy]dx = 0 dy (b) _xy − y² + (1 − xy) - 0 dx (c) (3x²y + 2xy + y³)dx + (x² + y²) dy = 0 = Consider the second order IVP given by (a) (b) y" + 2y' - 2y = 0, y(0) = 1, y'(0) = -1. Find the solution of the IVP. Calculate the Wronskian of the two solutions you found from the characteristic equation in part (a), and verify that it is indeed consistent with Abel's Theorem.
Transcribed Image Text:Solve the following DEs (in implicit form): (a) [x² + cos y ]dy + [2xy]dx = 0 dy (b) _xy − y² + (1 − xy) - 0 dx (c) (3x²y + 2xy + y³)dx + (x² + y²) dy = 0 = Consider the second order IVP given by (a) (b) y" + 2y' - 2y = 0, y(0) = 1, y'(0) = -1. Find the solution of the IVP. Calculate the Wronskian of the two solutions you found from the characteristic equation in part (a), and verify that it is indeed consistent with Abel's Theorem.
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