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Dy/dx = 4x - 3, y(1) = 0 A) y = 2x2 + x - 1 B) y = -x...
JMAP math
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dy/dx = 4x - 3, y(1) = 0

A) y = 2x2 + x - 1

B) y = -x2 + x - 2

C) y = 2x2 + x + 1

D) y = 2x2 - 3x + 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 = 4x - 3

Multiply both sides by dx,

dy = (4x - 3) dx

Integrating both sides,

∫dy = ∫(4x - 3) dx

y = 4x2/2 - 3x + c

y = 2x2 - 3x + c ------------ eqn(1)

Where c is the integration constant.

Since y(1) = 0,

0 = 2(1)2 - 3(1) + c

0 = 2 - 3 + c

0  = -1 + c

Add 1 to both sides,

c = 1

Thus, eqn(1) becomes:

y = 2x2 - 3x + 1

Ans D

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