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Vishrant Vasavada Grade: 11
        If dy/dx = x^2 + 2, then find the value of y in terms of x. It is given that initially, x = 0 and y = 3.
7 years ago

Answers : (1)

AskiitianExpert Shine
10 Points
										

Hi


dy/dx = x^2 + 2

integrating both sides w.r.t x, we get each term as follows:


Integration of dy/dx = y + a

                      x^2 = (x^3)/3  + b

                      2 = 2x + c                     (a,b and c are constants of integration)


Now, combining the terms and taking a,b and c on one side of equation and replacing the resulting constant as Z we get:


y= (x^3)/3 + 2x + Z


But we are given that y=3 when x=0

putting these values in above equation:


3=0 + 0 + Z

Z = 3


Hence, we get our answer as : y= (x^3)/3 + 2x + 3

7 years ago
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