Solve the following initial value problem: `C^(prime)(x)=2+0. 15 x ; C(0)=100`

Answer

`C(x)=2x+0.15 frac{x^2}{2}+100`

Explanation

We are given
`C^(prime)(x)=2+0. 15 x`

`rArr frac{dC}{dx} = 2+0.15x`


`rArr dC = (2+0.15x)dx`


Integrate both sides, we get,

`int dC = int (2+0.15x)dx`

`rArr C(x)=2x+0.15 frac{x^2}{2}+a` `- (1)` , where `a` is a constant term


We are already given that `C(0)=100`


Put `x=0` in `(1)` we get,
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