What is the general solution to the ODE

/[dy/dx = 2y+1?/]

Use separation of variables.

Is y' + xy = x separable?

we are given the ordinary differential equation of dy/dx = 2y+1. The ODE is variable separable which means x and y can be grouped altogether explicitly. In this case, the equation becomesdy / 2y + 1 = dx

1/2 ln (2y + 1) = x + ln Cln (2y + 1) = 2x + ln C2y + 1 = C e 2x y = (C e 2x - 1) / 2

The ODE y' + xy = x can be grouped into y' + x (y-1) = 0 'y' / y-1 = - xThis is variable separable