Separable Differential Equations
Separable Differential Equations
A separable differential equation has the form . It is called "separable" because the " stuff" can be moved to the left side, leaving the " stuff" on the right. Then, when the equation is multiplied by , the result is . Now both sides can be integrated with respect to the variable on that side. The resulting equation might be solvable for . An initial condition (coordinates of a point on the solution curve) can be applied as well.
Using the App: 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 -value and corresponding -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 will appear.
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.