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HP 48gII grafische rekenmachine Manual

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Blz. 14-3
Voer in:
'X^2' ` 'X^3-4*X^2-11*X+30' ` LDEC
De oplossing is:
dat kan worden vereenvoudigd tot
y = K
1
⋅e
–3x
+ K
2
⋅e
5x
+ K
3
⋅e
2x
+ (450⋅x
2
+330⋅x+241)/13500.
De functie DESOLVE
De rekenmachine geeft de functie DESOLVE (Differentiaalvergelijking SOLVer)
om bepaalde soorten differentiaalvergelijkingen op te lossen. De functie
vereist als invoer de differentiaalvergelijking en de onbekende functie en geeft
indien beschikbaar de oplossing voor de vergelijking. U kunt ook een vector
met daarin de differentiaalvergelijking en de beginvoorwaarden als invoer
voor DESOLVE geven in plaats van alleen een differentiaalvergelijking. De
functie DESOLVE is beschikbaar in het menu CALC/DIFF. Voorbeelden van
DESOLVE-toepassingen worden hieronder weergegeven in de RPN-modus.
Voorbeeld 1
–de volgende eerste orde ODE oplossen:
dy/dx + x
2
⋅y(x) = 5.
Gebruik in de rekenmachine:
'd1y(x)+x^2*y(x)=5' ` 'y(x)' ` DESOLVE
De gegeven oplossing is
{‘y(x) = (5*INT(EXP(xt^3/3),xt,x)+cC0)*1/EXP(x^3/3))’ }, die vereenvoudigd
kan worden tot
(
)
.)3/exp()3/exp(5)(
0
33
Cdxxxxy +⋅⋅−⋅=
∫
… 157 …


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