Verify that the function is a solution of the initial value problem. (a) y = x cos x; y' = cos(x) - y tan(x), y(π/4) = (π/4√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.
Chapter11: Differential Equations
Section11.2: Linear First-order Differential Equations
Problem 2YT: YOUR TURN Solve the initial value problem dydx+2xyxex2=0 with y(0)=3.
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Verify that the function is a solution of the initial value problem.
(a) y = x cos x;  y' = cos(x) - y tan(x), y(π/4) = (π/4√2)

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Consider the provided question,

(a)

We need to verify y=xcosx is the solution of the y'=cosx-ytanx;  yπ4=π42

 

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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,