2. In each of the following, verify that the given expression is an explicit or implicit solution of the ODE, and say which it is (explicit or implicit): (a) y' = 25+ y²; (b) 2xy + (x² - y)dy/dx = 0; (c) 2y' = y³ cos x; y = 5 tan(5x). y² – 2x²y = 1. y = (1 — sin x)-1/2.
2. In each of the following, verify that the given expression is an explicit or implicit solution of the ODE, and say which it is (explicit or implicit): (a) y' = 25+ y²; (b) 2xy + (x² - y)dy/dx = 0; (c) 2y' = y³ cos x; y = 5 tan(5x). y² – 2x²y = 1. y = (1 — sin x)-1/2.
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.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 4E
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Can someone please explain (b) to me? I don't know how to solve it so that I can find out that it is implicit. Thank you very much!
Transcribed Image Text:2. In each of the following, verify that the given expression is an explicit or
implicit solution of the ODE, and say which it is (explicit or implicit):
(a) y' = 25+ y²;
(b) 2xy + (x² − y)dy/dx = 0;
(c) 2y' = y³ cos x;
Y 5 tan(5x).
=
y² – 2x²y = 1.
Y
=
= (1 - sin x)-¹/2.
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How do I get 2y*dx/dt + (-4xy + y' * x^2) = 0 and y' = (1/ x^2)(2xy + y - 1)?
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