Solution 17214: Solving Second Order Differential Equations on the TI-89 Family, TI-92 Plus and Voyage™ 200 Graphing Calculator.
How do you solve a second order differential equations on a TI-89 Family, TI-92 Plus and Voyage 200 Graphing Calculator?
First and second order differential equations can be solved by using the deSolve( command.
1. First Order Example
Solver the equation y''+2y'+y=x^2.
Solution: Start by clearing the calculator's home screen and following the instructions below to solve using the deSolve( command.
- Press [CATALOG] and scroll to deSolve( or choose deSolve( from the (F3) 'Calc' menu.
- Enter y''+2y'+y=x^2, x, y) Note: To get ', press the [2ND] [ ' ].
- Press [ENTER] to display the answer. The variables @1, @2 are constants.
2. Second Order Example: A ball is tossed straight up from an initial height of 0.29 meters and with an initial velocity of 3.8m/s. Solve the second order differential equation below to model the height of the ball over time:
y"=-9.8, y(0)=.29, y'(0)=3.8
Solution: Start by clearing the calculator's home screen and following the instructions below to solve using the deSolve( command.
- Press [CATALOG] and scroll to deSolve( or choose deSolve( from the (F3) 'Calc' menu.
- Press [Y] then [2ND] [ ' ] [2ND] [ ' ] [=].
- Enter [(-)] 9.28 [CATALOG].
- Choose 'and' from the list and press [ENTER].
- Input the remaining equations separated by 'and'.
- After inputting the final equation type [ , ] [T] [ , ] [Y] [ ) ].
- Your display should read deSolve(y"=-9.8 and y(0)=.29 and y'(0)=3.8,t,y).
- Press [ENTER].
- The answer y=-4.9t2+3.8t+.29 is displayed.
Note: The TI-89 Family, TI-92 Plus and Voyage 200 can solve the following types of 1st and 2nd order differential equations:
1st Order: separable, linear, Bernoulli, y'=f(a*x+b*y), exact, integrating factor independent of x, integrating factor independent of y, and homogeneous.
2nd Order: linear constant coefficient (and a few variable coefficient), missing y, missing y', missing x, missing both y' and x.