Knowledge Base

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.