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Page 16-8
Example 2 -- Solve the second-order ODE:
d
2
y/dx
2
+ x (dy/dx) = exp(x).
In the calculator use:
‘
d1d1y(x)+x*d1y(x) = EXP(x)
’
`
‘
y(x)
’
`
DESOLVE
The result is an expression having two implicit integrations, namely,
For this particular equation, however, we realize that the left-hand side of the
equation represents d/dx(x dy/dx), thus, the ODE is now written:
d/dx(x dy/dx ) = exp x,
and
x dy/dx = exp x + C.
Next, we can write
dy/dx = (C + exp x)/x = C/x + e
x
/x.
In the calculator, you may try to integrate:
‘
d1y(x) = (C + EXP(x))/x
’
`
‘
y(x)
’
`
DESOLVE
The result is { ‘y(x) = INT((EXP(xt)+C)/xt,xt,x)+C0’ }, i.e.,
The variable ODETYPE
You will notice in the soft-menu key labels a new variable called
@ODETY
(ODETYPE). This variable is produced with the call to the DESOL function and
holds a string showing the type of ODE used as input for DESOLVE. Press
@ODETY
to obtain the string “
1st order linear
”.
Summary of Contents for 50G
Page 1: ...HP g graphing calculator user s guide H Edition 1 HP part number F2229AA 90006 ...
Page 130: ...Page 2 70 The CMDS CoMmanDS menu activated within the Equation Writer i e O L CMDS ...
Page 206: ...Page 5 29 LIN LNCOLLECT POWEREXPAND SIMPLIFY ...
Page 257: ...Page 7 20 ...
Page 383: ...Page 11 56 Function KER Function MKISOM ...
Page 715: ...Page 21 68 Whereas using RPL there is no problem when loading this program in algebraic mode ...
Page 858: ...Page L 5 ...