HP 48gII - Manual (Page 486)

Page 16-8
dy/dx + x 2 ⋅y(x) = 5.
In the calculator use:
'd1y(x)+x^2*y(x)=5' ` 'y(x)' ` DESOLVE
The solution provided is {‘y =
(INT(5*EXP(xt^3/3),xt,x)+cC0)*1/EXP(x^3/3))’ }, 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 ”.
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.
( )
. ) 3 / exp( 5 ) 3 / exp( ) (
0
3 3 cC dx x x x y + ⋅ ⋅ ⋅ − =
∫