HP 49g+ - Manual (Page 476)

Page 16-2
The result is ‘
∂
x(
∂
x(u(x)))+3*u(x)*
∂
x(u(x))+u^2=1/x
’. This format
shows up in the screen when the _Textbook option in the display setting
(
H@)DISP) is not selected. Press ˜ to see the equation in the Equation
Writer.
An alternative notation for derivatives typed directly in the stack is to use ‘d1’
for the derivative with respect to the first independent variable, ‘d2’ for the
derivative with respect to the second independent variable, etc. A second-
order derivative, e.g., d
2 x/dt 2 , where x = x(t), would be written as ‘d1d1x(t)’,
while (dx/dt) 2 would be written ‘d1x(t)^2’. Thus, the PDE ∂ 2 y/ ∂t 2 – g(x,y) ⋅
( ∂ 2 y/ ∂x 2 ) 2 = r(x,y), would be written, using this notation, as ‘d2d2y(x,t)-
g(x,y)*d1d1y(x,t)^2=r(x,y)’.
The notation using ‘d’ and the order of the independent variable is the
notation preferred by the calculator when derivatives are involved in a
calculation. For example, using function DERIV, in ALG mode, as shown next
DERIV(‘x*f(x,t)+g(t,y) = h(x,y,t)’,t), produces the following expression:
‘x*d2f(x,t)+d1g(t,y)=d3h(x,y,t)’. Translated to paper, this
expression represents the partial differential equation x
⋅(∂f/∂t) + ∂g/∂t = ∂h/∂t.
Because the order of the variable t is different in f(x,t), g(t,y), and h(x,y,t),
derivatives with respect to t have different indices, i.e., d2f(x,t), d1g(t,y), and
d3h(x,y,t). All of them, however, represent derivatives with respect to the
same variable.
Expressions for derivatives using the order-of-variable index notation do not
translate into derivative notation in the equation writer, as you can check by
pressing
˜ while the last result is in stack level 1. However, the calculator
understands both notations and operates accordingly regarding of the
notation used.
Checking solutions in the calculator
To check if a function satisfy a certain equation using the calculator, use
function SUBST (see Chapter 5) to replace the solution in the form ‘y = f(x)’ or
‘y = f(x,t)’, etc., into the differential equation. You may need to simplify the