TiNspire CX CAS : Solving 1. order Differential Equations – Step by Step

If we are asked to solve the 1. Order Differential Equation y’+4y=8 we see that it is Linear in y and thus use option B in Differential Equations Made Easy at www.TiNspireApps.com as shown below:

Next enter the coefficients 4 and 8 and leave the 2. box empty since we are not given any initial conditions.


To get the general solution :

If we are given this first order homogeneous Differential Equation :

dy/dx + 5yx^3 = 0 we think of it as dy/dx = – 5yx^3 which calls for Separable Differential Equations which are solved using option 3 as follows :

Here we add an initial condition which allows to find a particular solution:

and finally the separation of variables method yields the particular solution:

TiNspire CX : Euler Method (Differential Equations)

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:

(Don’t forget the * between y and (5-y)

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.

TiNspire CX Limit Solver

Use belows Limit Solver when asked to find a constant for which a limit exists. Ex: What is a in (x^2+x-a) /(x-2) as x approaches 2?

To find the constant a for which the limit exists using the TiNspire CX CAS use Calculus Made Easy at www.TinspireApps.com , select option 6 in the Limits menu :



When entering the above example, we find the Limit to be 5 when the constant a=6 .

TiNspire CX CAS: Nonhomogeneous, Nonlinear Cauchy Euler 3. order Differential Equation

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.

TiNSpire CX: Solve System of Differential Equations using LaPlace Transform – Step by Step

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:

Solving Fractions and Quadratics using the TiNSpire – Step by Step

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 :

  1. problem:

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:

and

It always works!

Quadratic equations can also be solved step by step. Here is one:

and

Even equations containing only variables can be solved (for x):

Cube root, other roots and radicals using the TiNSpire CX CAS

Say you need to find 3 radical 27 , that is to find the cube root of 27. Enter it as:

and it will display as

Similarly, the 4th root of 16 is entered :

and it is displayed as

And the 5th root of x is then entered as

to be displayed as

Nice and simple. In conclusion, radicals and roots can be dealt with using the handy root-function.

Projectile Motion with the TiNspire CX – Step by Step

Here is how to perform Projectile Motion using the TiNspire CX : Launch the Physics Made Easy from www.TinspireApps.com and go to the menu option 2: Kinematics – Linear and Rotational as shown below :

Next scroll down to “Projectile At Angle”. This menu option will do step by step analysis of the projectile given initial values such as Angle, Initial Velocity and Initial height.


Here is an example:

Now, if you are to find Initial Speed, Launch Angle etc just scroll further down in the menu as we have those scenarios covered too.

Differential Gleichungen Loesen – Schrittweise – mit dem Ti-Nspire CX CAS

Nehmen wir als Bespiel die homogene Differentialgleichung 2. Ordnung :

y” + 8y’ + 16y =0

Wir starten die TiNspire APP “Differentialgleichungen Leicht Gemacht” von www.Tinspireapps.com und gehen im Menu zu Option 4: Homogene Differentialgleichung.

Und geben einfach die DGL oben ein.

Um eine partikulaere Loesung zu finden gibt man die Anfangswert Bedingungen unten ein:

So leicht ist es schrittweise Loesungen zu Differentialgleichungen zu bekommen. Man kann diese Loesung mit der von Symbol-Lab vergleichen unter : https://www.symbolab.com/solver/ordinary-differential-equation-calculator/y”%2B8y’%2B16y%3D0