Checking Solutions In The Calculator - HP 48gII User Manual

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The result is

x(u(x)))+3*u(x)*

shows up in the screen when the _Textbook option in the display setting

(H@) D ISP) is not selected.

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.

order derivative, e.g., d

while (dx/dt)

would be written 'd1x(t)^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

x(u(x))+u^2=1/x

Press ˜ to see the equation in the Equation

, where x = x(t), would be written as 'd1d1x(t)',

Thus, the PDE ∂