HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 479

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) = ex 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: d2u(x)/dx2 + 3⋅u(x)⋅(du(x)/dx) + u(x)2 = 1/x, directly into the screen, use x x„ Ü~ „u „Ü ~„x™™™+3*~ „u„Ü ~„x x„ Ü~„u„ Ü ~„x u„ Ü ~„x™ Q2 , Å 1/ ~„x` Page 16-1