When solving a Differential Equation y’=y*(5-y) , y(0)=9 numerically using the Euler Method given stepsize of 0.1 use the Differential Equations made Easy app at www.tinspireapps.com and select Euler Method in the Menu as shown below :
Now you just enter the Differential Equation in the top box and the starting point and the step size in the bottom box as shown below:
The bottom box now shows the step by step solution of the Euler Method. Works correctly for any given Differential Equation.
Alternative to the Euler Method you may also the built-in Runga Kutta RK4 method.
To solve a 3. order Cauchy Euler Differential that is Nonhomogeneous and NonLinear you would use the Differential Equations Made Easy at www.TiNspireApps.com and enter the coefficients of the Differential Equations as follows:
As can be seen, the substitution y=x^n allows us to find the zeros of the homogeneous Differential Equation and its solution below. Now, we are after the nonhomogenous solution which involves find the 4 Wronskians W, W1, W2, W3 using the Variation of Parameter method:
After finding the 3 v_i, their integration allows us to find the final solution
Puuh, that was a lot of work…If you want to skip watch all the steps you might just jump straight to the final solution.
Say you have to classify nodes when studying the stability of Non-Linear Systems. Use the Differential Equations Made Easy App at www.TinspireApps.com under menu item 3 E . Enter the given System as follows in the two top boxes:
When plugging the critical points into the Jacobian we are able to compute the EigenValues that allow us to classify the nodes as stable, unstable, saddle point, center or spiral point.
Say you have to solve the system of Differential Equations shown in below’s image. Launch the Differential Equations Made Easy app (download at www.TiNspireApps.com) , go to Laplace Transforms in the menu and just type in as shown below:
Scrolling down to view all steps finally shows the correct final answer:
To solve a separable Differential Equation such as dy/dx + xy=0 or rewritten dy/dx = – x*y with initial condition y(0)=2 use the Differential Equation Made Easy app at www.TinspireApps.com , use menu option 1 3 (Separation of Variables) and enter as follows :
to finally get both the general and particular solutions.