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Question: why dsolve gives Error, (in dsolve) this is a bug on this ode with IC?

Question:why dsolve gives Error, (in dsolve) this is a bug on this ode with IC?

nm 11473 Maple 2025
ode dsolve differential-equations solvetools
3 hours ago
0

Never seen such a message before

Here is MWE, Trace shows it comes from (SolveTools:-PolynomialSystemSolvers:-PseudoResultant:-AttemptFactorization,2)

 

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1878 and is the same as the version installed in this computer, created 2025, September 28, 11:35 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

> 

ode:=diff(y(x),x$2)+3*y(x)+D(y)(3)=0;
IC:=y(1)+4*y(2)+y(4)=0;

diff(diff(y(x), x), x)+3*y(x)+(D(y))(3) = 0

y(1)+4*y(2)+y(4) = 0

> 

dsolve(ode)

x+(1/3)*3^(1/2)*(tan(3^(1/2)*x)-arctan(tan(3^(1/2)*x)))-((1/3)*(D(y(x)))(3)*(1+tan(3^(1/2)*x)^2)^(1/2)+(1+tan(3^(1/2)*x)^2)^(1/2)*y(x))*c__1-c__2 = 0

> 

dsolve([ode,IC])

Error, (in dsolve) this is a bug

> 

tracelast

 dsolve called with arguments: [diff(diff(y(x), x), x)+3*y(x)+(D(y))(3) = 0, y(1)+4*y(2)+y(4) = 0], arbitraryconstants = subscripted, atomizenames = true, build = false, numeric = false, type = none
 #(dsolve,80): error

 \`dsolve/IC\` called with arguments: [diff(diff(y(x), x), x)+3*y(x)+(D(y))(3) = 0, y(1)+4*y(2)+y(4) = 0], {y(x)}, skipimplicit = false, skippparticularsolforlinearODEs = true, solution = {}, usesolutions = particular and general
 #(\`dsolve/IC\`,53): return procname(_passed,':-usesolutions' =  "general and particular")

 \`dsolve/IC\` called with arguments: [diff(diff(y(x), x), x)+3*y(x)+(D(y))(3) = 0, y(1)+4*y(2)+y(4) = 0], {y(x)}, skipimplicit = false, skippparticularsolforlinearODEs = true, solution = {}, usesolutions = general and particular
 #(\`dsolve/IC\`,57): ans := procname(_passed,':-usesolutions = "general"');

 \`dsolve/IC\` called with arguments: [diff(diff(y(x), x), x)+3*y(x)+(D(y))(3) = 0, y(1)+4*y(2)+y(4) = 0], {y(x)}, skipimplicit = false, skippparticularsolforlinearODEs = true, solution = {}, usesolutions = general
 #(\`dsolve/IC\`,277): zz := map(op,{\`dsolve/IC/_C\`({ANS[i]},funcs,x,ics)});

 \`dsolve/IC/_C\` called with arguments: {y(x) = -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(3^(1/2)*x)^2)^(1/2)-3^(1/2)*tan(3^(1/2)*x)+3^(1/2)*arctan(tan(3^(1/2)*x))+3*_C[2]-3*x)/((1+tan(3^(1/2)*x)^2)^(1/2)*_C[1])}, {y(x)}, x, [y(1) = _C1, y(2) = _C2, y(4) = -_C1-4*_C2]
 #(\`dsolve/IC/_C\`,1): ans := \`dsolve/IC/_C/do\`(solns,depvars,t,inits,'evaluated_ans', "default",':-giveup = giveup');

 \`dsolve/IC/_C/do\` called with arguments: {y(x) = -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(3^(1/2)*x)^2)^(1/2)-3^(1/2)*tan(3^(1/2)*x)+3^(1/2)*arctan(tan(3^(1/2)*x))+3*_C[2]-3*x)/((1+tan(3^(1/2)*x)^2)^(1/2)*_C[1])}, {y(x)}, x, [y(1) = _C1, y(2) = _C2, y(4) = -_C1-4*_C2], evaluated_ans, default, giveup = giveup, usecansolve = false
 #(\`dsolve/IC/_C/do\`,103): csol := [\`ODEtools/Solve/EnvDropMultiplicity\`(eqns,consts)];

 \`ODEtools/Solve/EnvDropMultiplicity\` called with arguments: {-(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(3^(1/2))^2)^(1/2)-3^(1/2)*tan(3^(1/2))+3^(1/2)*(3^(1/2)-Pi)+3*_C[2]-3)/((1+tan(3^(1/2))^2)^(1/2)*_C[1]) = _C1, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(2*3^(1/2))^2)^(1/2)-3^(1/2)*tan(2*3^(1/2))+3^(1/2)*(2*3^(1/2)-Pi)+3*_C[2]-6)/((1+tan(2*3^(1/2))^2)^(1/2)*_C[1]) = _C2, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(4*3^(1/2))^2)^(1/2)-3^(1/2)*tan(4*3^(1/2))+3^(1/2)*(4*3^(1/2)-2*Pi)+3*_C[2]-12)/((1+tan(4*3^(1/2))^2)^(1/2)*_C[1]) = -_C1-4*_C2}, {_C1, _C2, _C[1], _C[2]}, keepalreadysolveduntouched = false, removelabel = false
 #(\`ODEtools/Solve/EnvDropMultiplicity\`,29): sol := :-solve(ee,X,_rest)

 solve called with arguments: {-(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(3^(1/2))^2)^(1/2)-3^(1/2)*tan(3^(1/2))+3^(1/2)*(3^(1/2)-Pi)+3*_C[2]-3)/((1+tan(3^(1/2))^2)^(1/2)*_C[1]) = _C1, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(2*3^(1/2))^2)^(1/2)-3^(1/2)*tan(2*3^(1/2))+3^(1/2)*(2*3^(1/2)-Pi)+3*_C[2]-6)/((1+tan(2*3^(1/2))^2)^(1/2)*_C[1]) = _C2, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(4*3^(1/2))^2)^(1/2)-3^(1/2)*tan(4*3^(1/2))+3^(1/2)*(4*3^(1/2)-2*Pi)+3*_C[2]-12)/((1+tan(4*3^(1/2))^2)^(1/2)*_C[1]) = -_C1-4*_C2}, {_C1, _C2, _C[1], _C[2]}, AllSolutions = FAIL, ConditionalSolutions = FAIL, DropMultiplicity = FAIL, Explicit = FAIL, MaxSols = FAIL, SolveOverReals = FAIL, SymbolicSolutions = true, TryHard = FAIL, UseAssumptions = false, domain = default, parameters = {}, parametric = false, split = false, useunits = FAIL
 #(solve,133): _MaxSols := oldmaxsols

 Engine:-Main called with arguments: {-(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(3^(1/2))^2)^(1/2)-3^(1/2)*tan(3^(1/2))+3^(1/2)*(3^(1/2)-Pi)+3*_C[2]-3)/((1+tan(3^(1/2))^2)^(1/2)*_C[1]) = _C1, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(2*3^(1/2))^2)^(1/2)-3^(1/2)*tan(2*3^(1/2))+3^(1/2)*(2*3^(1/2)-Pi)+3*_C[2]-6)/((1+tan(2*3^(1/2))^2)^(1/2)*_C[1]) = _C2, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(4*3^(1/2))^2)^(1/2)-3^(1/2)*tan(4*3^(1/2))+3^(1/2)*(4*3^(1/2)-2*Pi)+3*_C[2]-12)/((1+tan(4*3^(1/2))^2)^(1/2)*_C[1]) = -_C1-4*_C2}, {}, {_C1, _C2, _C[1], _C[2]}
 #(SolveTools:-Engine:-Main,37): sol := [SolveTools:-PolynomialSystem(eqns,vars,ineqs,':- maxsols' = \`if\`(type([_MaxSols],[{integer, infinity}]) and 0 < _MaxSols,_MaxSols,100))]

 PolynomialSystem:-ModuleApply called with arguments: {-(1/3)*(_X000003*(D(_Z))(3)*(1+tan(3^(1/2))^2)^(1/2)-3^(1/2)*tan(3^(1/2))+3^(1/2)*(3^(1/2)-Pi)+3*_X000004-3)/((1+tan(3^(1/2))^2)^(1/2)*_X000003) = _X000001, -(1/3)*(_X000003*(D(_Z))(3)*(1+tan(2*3^(1/2))^2)^(1/2)-3^(1/2)*tan(2*3^(1/2))+3^(1/2)*(2*3^(1/2)-Pi)+3*_X000004-6)/((1+tan(2*3^(1/2))^2)^(1/2)*_X000003) = _X000002, -(1/3)*(_X000003*(D(_Z))(3)*(1+tan(4*3^(1/2))^2)^(1/2)-3^(1/2)*tan(4*3^(1/2))+3^(1/2)*(4*3^(1/2)-2*Pi)+3*_X000004-12)/((1+tan(4*3^(1/2))^2)^(1/2)*_X000003) = -_X000001-4*_X000002}, {_X000001, _X000002, _X000003, _X000004}, {}, FAIL, backsubstitute = true, domain = absolute, engine = default, explicit = false, maxsols = 100, preprocess = true, preservelabels = false, tryhard = true
 #(SolveTools:-PolynomialSystem:-ModuleApply,15): sol := SolveTools:-PolynomialSystem:-Main(SolveTools:-Utilities:-New( equations,notz,SolveTools:-Utilities:-Intersect(vars,indets(equations ))),':-backsub' = reallybacksub,':-domain' = domain,':-maxsols' =  realmaxsols,':-engine' = engine,':-preprocess' = preprocess,':- tryhard' = tryhard);

 PolynomialSystem:-Main called with arguments: [{-(1/3)*(_X000003*(D(_Z))(3)*(1+tan(3^(1/2))^2)^(1/2)-3^(1/2)*tan(3^(1/2))+3^(1/2)*(3^(1/2)-Pi)+3*_X000004-3)/((1+tan(3^(1/2))^2)^(1/2)*_X000003)-_X000001, -(1/3)*(_X000003*(D(_Z))(3)*(1+tan(2*3^(1/2))^2)^(1/2)-3^(1/2)*tan(2*3^(1/2))+3^(1/2)*(2*3^(1/2)-Pi)+3*_X000004-6)/((1+tan(2*3^(1/2))^2)^(1/2)*_X000003)-_X000002, -(1/3)*(_X000003*(D(_Z))(3)*(1+tan(4*3^(1/2))^2)^(1/2)-3^(1/2)*tan(4*3^(1/2))+3^(1/2)*(4*3^(1/2)-2*Pi)+3*_X000004-12)/((1+tan(4*3^(1/2))^2)^(1/2)*_X000003)+_X000001+4*_X000002}, {3*(1+tan(3^(1/2))^2)^(1/2)*_X000003 <> 0, 3*(1+tan(2*3^(1/2))^2)^(1/2)*_X000003 <> 0, 3*(1+tan(4*3^(1/2))^2)^(1/2)*_X000003 <> 0}, {_X000001, _X000002, _X000003, _X000004}, {}, true, false, 1, {_X000001, _X000002, _X000003, _X000004}], backsub = true, domain = absolute, engine = default, maxsols = 100, preprocess = true, tryhard = true
 #(SolveTools:-PolynomialSystem:-Main,86): sol := [SolveTools:-PolynomialSystemSolvers:- PseudoResultant(SolveTools:-Utilities:- GetEquations(sys),SolveTools:-Utilities:- GetVariables(sys),SolveTools:-Utilities:- GetInequations(sys),':-maxsols' = maxsols,':- tryhard' = tryhard)];

 PseudoResultant:-ModuleApply called with arguments: {(_X000003*(D(_Z))(3)*(-2*cos(3^(1/2))+1+sec(3^(1/2)))+3*_X000001*_X000003*(-2*cos(3^(1/2))+sec(3^(1/2)))+3*_X000002*_X000003+3^(1/2)*tan(3^(1/2)))/cos(2*3^(1/2)), -(sec(4*3^(1/2))+sec(3^(1/2)))*_X000003*(D(_Z))(3)+3*(sec(4*3^(1/2))-sec(3^(1/2)))*_X000001*_X000003+12*_X000002*sec(4*3^(1/2))*_X000003+3^(1/2)*Pi+3^(1/2)*tan(4*3^(1/2))-3^(1/2)*tan(3^(1/2))}, {_X000001, _X000002, _X000003}, {_X000003 <> 0}, backsub = true, maxsols = 100, tryhard = true
 #(SolveTools:-PolynomialSystemSolvers:-PseudoResultant:-ModuleApply,25): SolveTools:-PolynomialSystemSolvers:-PseudoResultant:-ApplySubstitution ({},[],numer(tm1),notzero union map(xx -> denom(xx) <> 0,tm1), unknowns);

 ApplySubstitution called with arguments: {}, [], {_X000003*(D(_Z))(3)*sec(3^(1/2))+3*_X000001*sec(3^(1/2))*_X000003-2*_X000003*(D(_Z))(3)*cos(3^(1/2))-6*_X000001*_X000003*cos(3^(1/2))+3^(1/2)*tan(3^(1/2))+_X000003*(D(_Z))(3)+3*_X000002*_X000003, -_X000003*(D(_Z))(3)*sec(4*3^(1/2))+3*_X000001*sec(4*3^(1/2))*_X000003+12*_X000002*sec(4*3^(1/2))*_X000003+3^(1/2)*Pi+3^(1/2)*tan(4*3^(1/2))-_X000003*(D(_Z))(3)*sec(3^(1/2))-3*_X000001*sec(3^(1/2))*_X000003-3^(1/2)*tan(3^(1/2))}, {1 <> 0, _X000003 <> 0, cos(2*3^(1/2)) <> 0}, {_X000001, _X000002, _X000003}
 #(SolveTools:-PolynomialSystemSolvers:-PseudoResultant:-ApplySubstitution,48): eqns := map(SolveTools:-PolynomialSystemSolvers:-PseudoResultant:- AttemptFactorization,eqns,not0,unknowns);

 AttemptFactorization called with arguments: _X000003*(D(_Z))(3)*sec(3^(1/2))+3*_X000001*sec(3^(1/2))*_X000003-2*_X000003*(D(_Z))(3)*cos(3^(1/2))-6*_X000001*_X000003*cos(3^(1/2))+3^(1/2)*tan(3^(1/2))+_X000003*(D(_Z))(3)+3*_X000002*_X000003, {_X000003 <> 0, cos(2*3^(1/2)) <> 0}, {_X000001, _X000002, _X000003}
 #(SolveTools:-PolynomialSystemSolvers:-PseudoResultant:-AttemptFactorization,2): error \`this is a bug\`

Error, (in dsolve) this is a bug

 locals defined as: e = e

> 

 


 

Download dsolve_error_this_is_bug_2025_1_oct_2_2025.mw

Note that changing the IC to IC:=y(1)+4*y(2)=0; makes it work with no error.

It is only when adding y(4) does the error shows up.

For reference, this is what another software gives as solution. I am assuming it is correct but did not check
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