Texas Instruments TI-89 User Manual - Page 809

the general solution. soln|x=0 and y=0 ¸ true initialCondition is an equation of the form: d(right(eq)ìleft(eq),x)/ dependentVar (initialIndependentValue) = (d(left(eq)ìright(eq),y)) initialDependentValue !impdif(eq,x,y) ¸ The initialIndependentValue and initialDependentValue Done can be variables such as x0 and y0 that have no ode|y'=impdif(soln,x,y) ¸ stored values. Implicit differentiation can help true verify implicit solutions. DelVar ode,soln ¸ Done deSolve(2ndOrderOde and initialCondition1 and initialCondition2, independentVar, dependentVar) ⇒ a particular solution Returns a particular solution that satisfies 2ndOrderOde and has a specified value of the dependent variable and its first derivative at one point. deSolve(y''=y^(ë1/2) and y(0)=0 and y'(0)=0,t,y) ¸ 2øy 3/4 3 =t solve(ans(1),y) ¸ y= 22/3ø(3øt)4/3 4 and t,0 For initialCondition1, use the form: dependentVar (initialIndependentValue) = initialDependentValue For initialCondition2, use the form: dependentVar' (initialIndependentValue) = initial1stDerivativeValue deSolve(2ndOrderOde and boundaryCondition1 and boundaryCondition2, independentVar, dependentVar) ⇒ a particular solution Returns a particular solution that satisfies 2ndOrderOde and has specified values at two different points. deSolve(w''ì2w'/x+(9+2/x^2)w= xùe^(x) and w(p/6)=0 and w(p/3)=0,x,w) ¸ e p 3øxøcos(3øx) w= 10 e p 6øxøsin(3øx) ì 10 + x⋅ex 10 det( ) MATH/Matrix menu det(squareMatrix[, tol]) ⇒ expression Returns the determinant of squareMatrix. Optionally, any matrix element is treated as zero if its absolute value is less than tol. This tolerance is used only if the matrix has floating-point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, tol is ignored. • If you use ¥ ¸ or set the mode to Exact/Approx=APPROXIMATE, computations are done using floating-point arithmetic. • If tol is omitted or not used, the default tolerance is calculated as: 5Eë 14 ù max(dim(squareMatrix)) ù rowNorm(squareMatrix) det([a,b;c,d]) ¸ aød ìbøc det([1,2;3,4]) ¸ ë2 det(identity(3) ìxù[1,ë2,3; ë2,4,1;ë6,ë2,7]) ¸ ë(98øxòì55øxñ+ 12øx ì1) [1E20,1;0,1]!mat1 det(mat1) ¸ det(mat1,.1) ¸ [01.E20 11] 0 1.E20 Appendix A: Functions and Instructions 809