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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.

```
11 years ago

```							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
```
11 years ago
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