SOLUTION: If dy/dx is 6x^2+4x-5, and y=10 when x=2, find the value of y when x=3. please with full working

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Question 1152830: If dy/dx is 6x^2+4x-5, and y=10 when x=2, find the value of y when x=3. please with full working
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

If dy%2Fdx=6x%5E2%2B4x-5, then f%28x%29 is
y=2x%5E3%2B2x%5E2-5x

and y=10 when x=2,
let'c double check that:
y=2%2A2%5E3%2B2%2A2%5E2-5%2A2
y=2%2A8%2B2%2A4-10
y=16%2B8-10
y=24-10
y=14=> y is not =10 when x=2,must be: y=14


find the value of y when x=3.
y=2%2A3%5E3%2B2%2A3%5E2-5%2A3
y=2%2A27%2B2%2A9-15
y=54%2B18-15
y=57

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

            It is very standard Calculus problem, typical for beginner Calculus students,
            and the solution by @MathLover1 is   A B S O L U T E L Y   W R O N G.

            Below find the correct solution,  instead.


Consider ANTIderivative, which is the general solution to the given differential equation

    y = 2x^3 + 2x^2 - 5x + C,    (1)

where C is an arbitrary constant.


We define the value of this constant from the given condition y= 10 at x= 2.


Substitute x= 2 into (1) to get

    10 = 2^2^3 + 2*2^2 - 5x + c,

    10 = 2*8 + 2*4 - 5*2 + C = 16 + 8 - 10 + C = C + 14,

which implies

    C = 10 - 14 = -4.


So, the specific solution to the given differential equation under the given condition at the point x= 2 is

    y = 2x^3 + 2x^2 - 5x - 4.    (2)


Now the value of y at x= 3 is

    y = 2*3^3 + 2*3^2 - 5*3 - 4 = 53.      ANSWER

Solved,  answered,  explained  (in all details)  and completed.


/\/\/\/\/\/\/\/\/

Having this text before your eyes,  printed or in the screen of your computer,
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You may use this post for many other similar problems,  with the equal success.


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