Separable Equation with Initial Condition

Separable Equation with Initial Condition

For:

$$\frac{dy}{dx}=f(x)g(y),\quad y(x_0)=y_0$$

the solution can be written as:

$$\int_{y_0}^{y}\frac{du}{g(u)}=\int_{x_0}^{x}f(t)\,dt$$

Usage

- Avoids explicitly calculating the arbitrary constant and is useful for initial-value problems.