Solve the following differential equation: `sqrt(a+x)dy+x\ dx=0`

Explanation

`sqrt{a+x} d y+x d x=0 `


`Rightarrow sqrt{a+x} d y=-x d x `


`Rightarrow d y=frac{-x}{sqrt{a+x}} d x `


`Rightarrow d y=-frac{(x+a-a)}{sqrt{a+x}} d x `


`Rightarrow d y=-(sqrt{a+x}-frac{a}{sqrt{a+x}}) d x `


By Integrating, we obtain


`int d y=-int(sqrt{a+x}-frac{a}{sqrt{a+x}}) d x `


`Rightarrow y=-frac{2(a+x)^{frac{3}{2}}}{3}+2 a sqrt{a+x}+C `


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