A [i]separable differential equation[/i] has the form [math]\frac{dy}{dx}=f\left(x\right)\cdot g\left(y\right)[/math]. It is called "separable" because the "[math]y[/math] stuff" can be moved to the left side, leaving the "[math]x[/math] stuff" on the right. Then, when the equation is multiplied by [math]dx[/math], the result is [math]\frac{1}{g\left(y\right)}dy=f\left(x\right)dx[/math]. Now both sides can be integrated with respect to the variable on that side. The resulting equation might be solvable for [math]y[/math]. An initial condition (coordinates of a point [math](x_0,y_0)[/math] on the solution curve) can be applied as well.[br][br][b]Using the App[/b]: Begin by entering the "x part" and the "y part" of the derivative expression in the appropriate boxes. You will likely have to "undo" a given expression to separate the terms, but you'll have to do this anyway to solve the DE. Also enter an initial condition as an [math]x[/math]-value and corresponding [math]y[/math]-value satisfying the solution. Follow the steps in blue to see the progression of the solution. If a closed-form solution is possible, it will be given; otherwise [math]y=?[/math] will appear.[br][br]On the right, a solution curve will be drawn (if one exists). You can drag the Initial Condition point around to see the effect on the particular solution. A slope field is overlaid to indicate the family of solutions. You can adjust the density of the slope segments using the slider; move all the way to the left to turn the slope field off completely.