# Tracing curves on fieldplots in Maple
# June 7, 2006
# 
> with(DETools)
[AreSimilar, DEnormal, DEplot, DEplot3d, DEplot_polygon, DFactor, DFactorLCLM, 



  DFactorsols, Dchangevar, FunctionDecomposition, GCRD, Gosper, Heunsols, 



  Homomorphisms, IsHyperexponential, LCLM, MeijerGsols, 



  MultiplicativeDecomposition, 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, 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]
# First I will define the equation; we could just type the equation in the plot but generally it is better to define the various parts separately to help pinpoint typos.  Note the difference between the "set equal"  :=  and the "equation equal"  =
> eqn := diff(y(x), x) = -y(x)-sin(x)
                        d                       

                eqn := --- y(x) = -y(x) - sin(x)

                        dx                      
# I will now define the list of initial conditions (the starting points) which must be a "list of lists" so note there are brackets inside brackets.
> initcond := [[y(-2.5) = 2], [y(-1.5) = 2], [y(-.5) = 2], [y(.5) = 2], [y(1.5) = 2], [y(2.5) = 2], [y(-2.5) = 1], [y(-2) = -2], [y(-1) = -2], [y(0) = -2], [y(1) = -2], [y(2) = -2]]
initcond := [[y(-2.5) = 2], [y(-1.5) = 2], [y(-0.5) = 2], [y(0.5) = 2], 



  [y(1.5) = 2], [y(2.5) = 2], [y(-2.5) = 1], [y(-2) = -2], [y(-1) = -2], 



  [y(0) = -2], [y(1) = -2], [y(2) = -2]]
# Now for the plot:
> DEplot(eqn, y(x), x = -3 .. 3, initcond, y = -3 .. 3)

# Read the help file on DEplot for lots of options one can use to change the colors, sizes, etc.