HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 480

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 secondorder derivative, e.g., d2x/dt2, where x = x(t), would be written as 'd1d1x(t)', while (dx/dt)2 would be written 'd1x(t)^2'. Thus, the PDE ∂2y/∂t2 - g(x,y)⋅ (∂2y/∂x2)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 Page 16-2