If y' = 6x - 3 and y(2)= 4,then y =
A) 6.
B) 3 - 3x.
C) 3 - 3x + 2.
D) 3 - 3x - 2.
E) 6 - 3x + 2.

Name: If y' = 6x - 3 and y(2)= 4,then y = A) 6. B) 3 - 3x. C) 3 - 3x + 2. D) 3 - 3x - 2. E) 6 - 3x + 2.
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Question

If y' = 6x - 3 and y(2)= 4,then y =
A) 6. 
B) 3 - 3x. 
C) 3 - 3x + 2. 
D) 3 - 3x - 2. 
E) 6 - 3x + 2.

Quizplus · Accepted Answer

Using the given initial condition, we can find the constant of integration:

y' = 6x - 3

Integrating with respect to x:

y = 3x^2 - 3x + C

Using y(2) = 4 to solve for C:

4 = 3(2)^2 - 3(2) + C
C = -2

Therefore, the solution to the differential equation is:

y = 3x^2 - 3x - 2

which matches choice D.

If Y' = 6x - 3 and Y(2)= 4,then Y