Texas Instruments TI-89 User Manual - Page 808
DelType, DelVar, deSolve, To type a prime symbol, press
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DelType DelType var_type Deletes all unlocked variables of the type specified by var_type. Note: Possible values for var_type are: ASM, DATA, EXPR, FUNC, GDB, LIST, MAT, PIC, PRGM, STR, TEXT, AppVar_type_name, All. Deltype "LIST" ¸ Done DelVar CATALOG DelVar var1[, var2] [, var3] ... Deletes the specified variables from memory. 2! a ¸ (a+2)^2 ¸ DelVar a ¸ (a+2)^2 ¸ 2 16 Done (a + 2)ñ deSolve() MATH/Calculus menu deSolve(1stOr2ndOrderOde, independentVar, dependentVar) ⇒ a general solution Note: To type a prime symbol ( ' ), press 2 È. Returns an equation that explicitly or implicitly specifies a general solution to the 1st- or 2ndorder ordinary differential equation (ODE). In the ODE: • Use a prime symbol ( ' , press 2 È) to denote the 1st derivative of the dependent variable with respect to the independent variable. • Use two prime symbols to denote the corresponding second derivative. deSolve(y''+2y'+y=x^2,x,y) ¸ y=(@1øx+@2)øeë x+xñì4øx+6 right(ans(1))!temp ¸ (@1øx+@2)øeë x+xñì4øx+6 d(temp,x,2)+2ùd(temp,x)+tempìx^2 ¸ 0 DelVar temp ¸ Done The ' symbol is used for derivatives within deSolve() only. In other cases, use d( ) . The general solution of a 1st-order equation contains an arbitrary constant of the form @k, where k is an integer suffix from 1 through 255. The suffix resets to 1 when you use ClrHome or ƒ 8: Clear Home. The solution of a 2nd-order equation contains two such constants. Apply solve() to an implicit solution if you want to try to convert it to one or more equivalent explicit solutions. deSolve(y'=(cos(y))^2ùx,x,y) ¸ tan(y)= xñ 2 +@3 When comparing your results with textbook or manual solutions, be aware that different methods introduce arbitrary constants at different points in the calculation, which may produce different general solutions. solve(ans(1),y) ¸ ( ) y=tanê x 2 + 2i@ 3 2 +@n1øp ans(1)|@3=cì1 and @n1=0 ¸ ( ) y=tanê xñ +2ø(cì 1) 2 deSolve(1stOrderOde and initialCondition, independentVar, dependentVar) ⇒ a particular solution Returns a particular solution that satisfies 1stOrderOde and initialCondition. This is usually easier than determining a general solution, substituting initial values, solving for the arbitrary constant, and then substituting that value into sin(y)=(yùe^(x)+cos(y))y'!ode ¸ sin(y)=(exøy+cos(y))øy' deSolve(ode and y(0)=0,x,y)!soln ¸ ë(2øsin(y)+yñ) 2 =ë(exì1)øeëxøsin(y) 808 Appendix A: Functions and Instructions