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 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:
Say your teacher has some fancy fractions to solve for you and you have a volleyball game , play practice and to prepare for the SAT next Saturday. So you take out your TiNspire CX CAS, launch the STEP BY STEP EQUATION SOLVER app from www.TiNspireApps.com and get a quick lesson on how to solve those fractions…which turns out not too difficult after following the provided steps below:
We select option 5 :
to get 5/14 . The trick is to multiply the given fractions by the product of their denominators (bottoms) to get a much easier equation to solve.
Here is another one:
It always works!
Quadratic equations can also be solved step by step. Here is one:
Even equations containing only variables can be solved (for x):