(2.1.1)(2.1.1)
O O
(2.2)(2.2)AreSimilar, DEnormal, DEplot, DEplot3d, DEplot_polygon, DFactor, DFactorLCLM,
DFactorsols, Dchangevar, FunctionDecomposition, GCRD, Gosper, Heunsols,
Homomorphisms, IVPsol, IsHyperexponential, LCLM, MeijerGsols,
MultiplicativeDecomposition, ODEInvariants, PDEchangecoords,
PolynomialNormalForm, RationalCanonicalForm, ReduceHyperexp, RiemannPsols,
Xchange, Xcommutator, Xgauge, Zeilberger, abelsol, adjoint, autonomous, bernoullisol,
buildsol, buildsym, canoni, caseplot, casesplit, checkrank, chinisol, clairautsol,
constcoeffsols, convertAlg, convertsys, dalembertsol, dcoeffs, de2diffop, dfieldplot,
diff_table, diffop2de, dperiodic_sols, dpolyform, dsubs, eigenring,
endomorphism_charpoly, equinv, eta_k, eulersols, exactsol, expsols, exterior_power,
firint, firtest, formal_sol, gen_exp, generate_ic, genhomosol, gensys, hamilton_eqs,
hypergeomsols, hyperode, indicialeq, infgen, initialdata, integrate_sols, intfactor,
invariants, kovacicsols, leftdivision, liesol, line_int, linearsol, matrixDE, matrix_riccati,
maxdimsystems, moser_reduce, muchange, mult, mutest, newton_polygon, normalG2,
ode_int_y, ode_y1, odeadvisor, odepde, parametricsol, particularsol, phaseportrait,
poincare, polysols, power_equivalent, rational_equivalent, ratsols, redode, reduceOrder,
reduce_order, regular_parts, regularsp, remove_RootOf, riccati_system, riccatisol,
rifread, rifsimp, rightdivision, rtaylor, separablesol, singularities, solve_group,
super_reduce, symgen, symmetric_power, symmetric_product, symtest, transinv,
translate, untranslate, varparam, zoom
Direction Fields and Graphical Solutions (Sections 1.3 and 5.4 of
Nagle/Saff/Snider)
Many introductory courses begin by trying to develop the student's understanding of what a
differential equation is, what it means for a function to solve an ODE, and how to perform some
analysis directly from the differential equation. Graphical methods are commonly employed in these
discussions. The Maple command DEplot, from the DEtools package, provides a comprehensive
interface for most graphical needs.
To begin, consider the first order (linear) differential equation
ODE d diff y x , x = x
2