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Dy/dx = -2x - 1, y(-1) = -1 A) y = 2x2 + 3x + 3 B) y ...
JMAP math
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dy/dx = -2x - 1, y(-1) = -1

A) y = 2x2 + 3x + 3

B) y = x2 + 2x + 1

C) y = x2 + x - 2

D) y = -x2 - x - 1

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judziy
Asked by judziyrep:1.7K
University of Benin Nigeria
25 June 2020

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peter
Peter answeredrep:1.6K
University of Lagos Nigeria
12 August 2020
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dy/dx = -2x - 1

Multiply both sides by dx,

dy = (-2x - 1) dx

Integrating both sides,

∫dy = ∫(-2x - 1) dx

y = -2x2/2 - x + c

y = - x2 - x + c ------------ eqn(1)

Where c is the integration constant.

Since y(-1) = -1,

-1 = - (-1)2 - (-1) + c

-1 = - 1 + 1 + c

-1 = 0 + c

c = -1

Thus, eqn(1) becomes:

y = - x2 - x - 1

Ans D

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