HP 48gII - Manual (Page 479)

Page 16-1
Chapter 16
Differential Equations
In this Chapter we present examples of solving ordinary differential equations
(ODE) using calculator functions. A differential equation is an equation
involving derivatives of the independent variable. In most cases, we seek the
dependent function that satisfies the differential equation.
Basic operations with differential equations
In this section we present some uses of the calculator for entering, checking
and visualizing the solution of ODEs.
Entering differential equations
The key to using differential equations in the calculator is typing in the
derivatives in the equation. The easiest way to enter a differential equation is
to type it in the equation writer. For example, to type the following ODE:
(x-1)
⋅(dy(x)/dx) 2 + 2 ⋅x⋅y(x) = e x sin x, use:
‚O „ Ü~ „x -1 ™™™*‚¿ ~„x
™~„y„Ü~„x™™ Q2 ™™+2*
~„ x * ~„ y „Ü~„x ™™™™
‚= „¸ ~„ x ™*S~„x `
The derivative dy/dx is represented by
∂
x(y(x)) or by d1y(x)
. For
solution or calculation purposes, you need to specify y(x) in the expression,
i.e., the dependent variable must include its independent variable(s) in any
derivative in the equation.
You can also type an equation directly into the stack by using the symbol
∂ in
the derivatives. For example, to type the following ODE involving second-
order derivatives: d
2 u(x)/dx 2 + 3
⋅
u(x)
⋅(
du(x)/dx) + u(x) 2 = 1/x, directly into
the screen, use:
³‚∂ ~„x„Ü‚¿~„x„ Ü~ „u
„Ü ~„x™™™+3*~ „u„Ü
~„x™*‚¿~„x„ Ü~„u„ Ü
~„x ™™ +~„u„ Ü ~„x™ Q2
‚ Å 1/ ~„x`