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Dy/dx = -2x + 3, y(3) = 3
JMAP math differential-equation
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dy/dx = -2x + 3, y(3) = 3

A) y = x2 + 3x + 1

B) y = x2 + 2x - 2

C) y = -x2 + 3x + 3

D) y = x2 + 2x + 1

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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 26 June 2020
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dy/dx = -2x + 3

Multiply both sides by dx,

dy = (-2x - 1) dx

Integrating both sides,

∫dy = ∫(-2x + 3) dx

y = -2x2/2 + 3x + c

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

Where c is the integration constant.

Since y(3) = 3,

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

3 = - 9 + 9 + c

3 = 0 + c

c = 3

Thus, eqn(1) becomes:

y = - x2 + 3x + 3

Ans C

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