Question 1152830
.


            It is very standard Calculus problem, typical for beginner Calculus students,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and the solution by @MathLover1 is &nbsp;&nbsp;<U>A B S O L U T E L Y &nbsp;&nbsp;W R O N G</U>.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Below find the correct solution, &nbsp;instead.



<pre>
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.      <U>ANSWER</U>
</pre>

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



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