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Dy/dx = 4x + 2, y(0) = 0
JMAP math differential-equation
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dy/dx = 4x + 2, y(0) = 0

A) y = 2x2 + 2x

B) y = 2x2 + 3x - 3

C) y = -2x2 + 3x + 1

D) y = 2x2 + x

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judziy
Asked by judziyrep:213
University of Benin 25 June 2020

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peter
Peter answeredrep:202
School not set 25 June 2020
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dy/dx = 4x + 2

Multiply both sides by dx,

dy = (4x + 2) dx

Integrating both sides,

∫dy = ∫(4x + 2) dx

y = 4x2/2 + 2x + c

y = 2x2 + 2x + c ------------ eqn(1)

Where c is the integration constant.

Since y(0) = 0,

0 = 2(0)2 + 2(0) + c

0 = 0 + c

c = 0

Thus, eqn(1) becomes:

y = 2x2 + 2x

Ans A

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