Please answer the highlighted problem! 1. Verify that the given functions y₁ and y2 satisfy the given homogeneous di erentialequation.(a) y₁(x) = e, Y₂(x) = e¯¤; y - y = 0.(b) y₁(x) = cos 2x, y2(x) = sin 2x;(c) y₁(x) = e` cos x, y₂(x) = ey2(x) =(d) y₁(x) = x−¹,= xy + 4y = 0.sin x; y + 2y + 2y = 0.−²; y + ¼y + 2²/2y = 0.

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Advanced Math

Please answer the highlighted problem!

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 11E

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Question

Please answer the highlighted problem!

1. Verify that the given functions y₁ and y2 satisfy the given homogeneous di erential
equation.
(a) y₁(x) = e, Y₂(x) = e¯¤; y - y = 0.
(b) y₁(x) = cos 2x, y2(x) = sin 2x;
(c) y₁(x) = e` cos x, y₂(x) = e
y2(x) =
(d) y₁(x) = x−¹,
= x
y + 4y = 0.
sin x; y + 2y + 2y = 0.
−²; y + ¼y + 2²/2y = 0.

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