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Question: Can this Jacobi Differential equation be solved?

Question:Can this Jacobi Differential equation be solved?

Ronan 827 Maple 16
differential-equation jacobian
March 28 2017
0

I have been trying to find a solution for the equation below. Is there a non numerical explicit solution?
 

restart

with(DEtools)

[AreSimilar, Closure, DEnormal, DEplot, DEplot3d, DEplot_polygon, DFactor, DFactorLCLM, DFactorsols, Dchangevar, Desingularize, 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]

 (1)

``

sol := (JacobiCN((1/10)*sqrt(5)*sqrt(2)*t, (1/3)*sqrt(3))*sqrt(5)+2*sqrt(2))/(JacobiCN((1/10)*sqrt(5)*sqrt(2)*t, (1/3)*sqrt(3))*sqrt(5)+5*sqrt(2))

(JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))*5^(1/2)+2*2^(1/2))/(JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))*5^(1/2)+5*2^(1/2))

 (2)

sol1 := diff(psi(t), t) = sol

diff(psi(t), t) = (JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))*5^(1/2)+2*2^(1/2))/(JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))*5^(1/2)+5*2^(1/2))

 (3)

odeadvisor(sol1, psi(t))

[_quadrature]

 (4)

sol2 := dsolve({sol1, psi(0) = 0})

psi(t) = Int((JacobiCN((1/10)*_z1*10^(1/2), (1/3)*3^(1/2))*5^(1/2)+2*2^(1/2))/(JacobiCN((1/10)*_z1*10^(1/2), (1/3)*3^(1/2))*5^(1/2)+5*2^(1/2)), _z1 = 0 .. t)

 (5)

``

``

sol3 := convert(sol, parfrac)

1-(3/5)*2^(1/2)*5^(1/2)/(JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))+2^(1/2)*5^(1/2))

 (6)

sol4 := diff(psi(t), t) = sol3

diff(psi(t), t) = 1-(3/5)*2^(1/2)*5^(1/2)/(JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2))+2^(1/2)*5^(1/2))

 (7)

dsolve({sol4, psi(0) = 0})

psi(t) = Int(-(3/5)*10^(1/2)/(JacobiCN((1/10)*_z1*10^(1/2), (1/3)*3^(1/2))+10^(1/2)), _z1 = 0 .. t)+t

 (8)

sol5 := diff(psi(t), t) = 3*sqrt(2)*sqrt(5)/(5*(JacobiCN((1/10)*sqrt(5)*sqrt(2)*t, (1/3)*sqrt(3))+sqrt(5)*sqrt(2)))

diff(psi(t), t) = 3*2^(1/2)*5^(1/2)/(5*2^(1/2)*5^(1/2)+5*JacobiCN((1/10)*5^(1/2)*2^(1/2)*t, (1/3)*3^(1/2)))

 (9)

odeadvisor(sol5)

[_quadrature]

 (10)

dsolve({sol5})

{psi(t) = Int((3/5)*10^(1/2)/(JacobiCN((1/10)*t*10^(1/2), (1/3)*3^(1/2))+10^(1/2)), t)+_C1}

 (11)

``


 

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