7YDEswithClasspad


 * Solving DEs with Classpad**

The calculator can either give a ** general solution ** or a ** particular solution ** to a differential equation.

You can solve DEs either by typing the instruction line ( Example 1 ) or interactively ( Example 2 ).

Example 1

math \text{Solve } \dfrac{dy}{dt} = 3t+2 math given the initial condition that y = 3 In the MAIN screen, Go to the ACTION menu, the EQUATIONS submenu and select **dSolve**

Instead of dy/dx (or dy/dt in this case), the calculator expects **y'** notation. The **'** symbol is in the virtual keyboard, **mth** tab, then select **CALC** from the bottom row ( see Figure 1 )

{Notice you can also select **dSolve** from here **(DSlv)** instead of from the menus}

Enter:
 * dSolve(y' = 3t + 2, t, y)**

{ Make sure you use variables for **t** and **y**, not letters from the **abc** keyboard} {Make sure you enter the __independent variable__ (**t**) before the __dependent variable__ (**y**)}

Notice ( Figure 2 ) that this gives the **general solution** with the constant of integration included { const(1) } which you would write as **c**.

To get the **particular solution** :​ Enter
 * dSolve(y' = 3t + 2, t, y, t=0, y=3)**

Example 2

math \text{Solve } \dfrac{dy}{dt} = 3t+2 math given the initial condition that y = 3 In the MAIN screen, Go to the INTERACTIVE menu, the EQUATIONS submenu and select **dSolve**

To get the **general solution** : Enter: Equation: **y'=3t+2** inde var: **t** Depe var: **y**
 * No condition**

Then **Ok**

To get the **particular solution** : Enter: Equation: **y'=3t+2** inde var: **t** Depe var: **y** Condition: **t=0,y=3**
 * Include condition**

Then **Ok**

Example 3

math \text{Solve } f''(x)=\sin(x) math given the conditions f(0) = 2, f '(0) = 0

In the MAIN screen, Go to the INTERACTIVE menu, the EQUATIONS submenu and select **dSolve**

To get the **general solution** : Enter: Equation: **y''=sin(x)** inde var: **x** Depe var: **y**
 * No condition**

Then **Ok**

To get the **particular solution** : Enter: Equation: **y''=sin(x)** inde var: **x** Depe var: **y** Condition: **x=0,y=2,y'=0**
 * Include condition**

Then **Ok**

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