Hp 48g Graphing Calculator Uživatelský manuál stáhnout pdf (Strana 229)

100

101

6. Enter the initial value for the solution variable.

7. Enter an acceptable error tolerance.

8. (Optional:) Enter a step size. Normally, the solver computes an

appropriate step size.

9. Press SOLVE.

Example: Solve this equation for y{\) given that ?/(0) = 2:

y' = i + y

CTfsoivEi m

(ENTER)(g) 2 (ENTER)

SOLVE V(TJ=FCT,V)

F= ■ T+Y '

INDEP: T INIT: 0 FINAL: 1

SDLN: V INIT: 2 FINHLif

TDL:.0001 STEP: Df It _ STIFF

6.15477759086

BBgmHHmiiiiiiiiiiHiiiim^

How accurate is the answer? The general solution to the differential

equation

y' = t + y

y = ce t - 1

Where c is an arbitrary constant. The given initial conditions were

2 = ce° — 0 — 1. Solving for c and substituting back into the general

solution, the solution equation is

y = 3e* — t — I

Solving for !/(l), returns 3e — 1 — 1 = 6.15484548538. Comparing the

results you can see there is an error of approximately 0.000068 which

is well within the specified error tolerance of 0.0001.

Solving a Stiff Initial-Value Problem

Some differential equations may seem to take forever to solve. If this

happens, the equations may be stiff. Use the stiff function to solve the

equation.

To use the stiff fynction:

1. Press (7^(S0LVE~)

2. Select So I ye dit f eq„

Differential Equations 19-3

1 2 ... 224 225 226 227 228 229 230 231 232 233 234 ... 611 612

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