Note

For the solution, the solve function returns an expression or value for the expression (Exp/Eq) input as its argument. The message “More solutions may exist” will appear on the display when a value is returned as the solution, because there may be multiple solutions.

The solve function can return a maximum of 10 solutions in the case of values.

Example: To solve cos (x) = 0.5 for x (initial value: 0)

(Angle unit setting: Deg)

udSolve [Action][Equation/Inequality][dSolve]

Function: Solves first, second or third order ordinary differential equations, or a system of first order differential equations.

Syntax: dSolve(Eq, independent variable, dependent variable [, initial condition-1, initial condition-2][, initial condition-3, initial condition-4][, initial condition-5, initial condition-6] [ ) ]

dSolve({Eq-1, Eq-2}, independent variable, {dependent variable-1, dependent variable-2} [, initial condition-1, initial condition-2, initial condition-3, initial condition-4] [ ) ]

•If you omit the initial conditions, the solution will include arbitrary constants.

•Input all initial conditions equations using the syntax Var = Exp. Any initial condition that uses any other syntax will be ignored.

Example: To solve a differential equation y’ = x, where y = 1 when x = 0

Example: To solve the system of first order differential equations y’ = y + z, z’ = y – z, where “x” is the independent variable, “y” and “z” are the dependent variables, and the initial conditions are y = 3 when x = 0, and z = '2 – 3 when x = 0

urewrite [Action][Equation/Inequality][rewrite]

Function: Moves the right side elements of an equation or inequality to the left side.

Syntax: rewrite(Eq/Ineq/List [ ) ]

Example: To move the right side elements of x + 3 = 5x – x2 to the left side

uexchange [Action][Equation/Inequality][exchange]

Function: Swaps the right-side and left-side elements of an equation or inequality.

Syntax: exchange(Eq/Ineq/List [ ) ]

Example: To swap the left-side and right-side elements of 3 > 5x – 2y

ueliminate [Action][Equation/Inequality][eliminate]

Function: Solves one equation with respect to a variable, and then replaces the same variable in another expression with the obtained result.

Syntax: eliminate(Eq/Ineq/List-1, variable, Eq-2 [ ) ]

Example: To transform y = 2x + 3 to x =, and substitute the result into 2x + 3y = 5

Chapter 2: Main Application

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