`dy/dx = x+3` Solve the differential equation

`(dy)/dx = x + 3`

This differential equation is separable since it can be rewritten in the form

`N(y)dy = M(x) dx`

So separating the variables, the equation becomes

`dy = (x+3)dx`

Integrating both sides, it result to

`int dy = int (x+3)dx`

`y+C_1 = x^2/2+3x+C_2`

Isolating the y, it becomes

`y = x^2/2 +3x+C_2-C_1`

Since C1 and C2 represents any number, it can be expressed as a single constant C.

`y = x^2/2 + 3x + C`

Therefore, the general solution of the given differential equation is `y=x^2/2 + 3x+C` .