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2.1517   ODE No. 1517

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

x3y(3)(x)−2x3+x2y″(x)+2xy′(x)−y(x)+log⁡(x)=0 ✓ Mathematica : cpu = 0.40514 (sec), leaf count = 1656

{{y(x)→c3xRoot[#13−2#12+3#1−1&,3]+c2xRoot[#13−2#12+3#1−1&,2]+c1xRoot[#13−2#12+3#1−1&,1]+(−2447+(884−340Root[#13−2#12+3#1−1&,1]+99Root[#13−2#12+3#1−1&,1]2)Root[#13−2#12+3#1−1&,3]+(147−721Root[#13−2#12+3#1−1&,1]−93Root[#13−2#12+3#1−1&,1]2)Root[#13−2#12+3#1−1&,3]2+Root[#13−2#12+3#1−1&,2](757+1398Root[#13−2#12+3#1−1&,3]+(−1129+2149Root[#13−2#12+3#1−1&,1]+523Root[#13−2#12+3#1−1&,1]2)Root[#13−2#12+3#1−1&,3]2)+Root[#13−2#12+3#1−1&,2]2(470−1794Root[#13−2#12+3#1−1&,3]+1581Root[#13−2#12+3#1−1&,3]2+Root[#13−2#12+3#1−1&,1](−1502+3905Root[#13−2#12+3#1−1&,3]−4526Root[#13−2#12+3#1−1&,3]2)))log⁡(x)+72160x3−2(5199x3+9833)Root[#13−2#12+3#1−1&,3]2+(6413−49216x3)Root[#13−2#12+3#1−1&,2]2Root[#13−2#12+3#1−1&,3]2+(47228x3+39905)Root[#13−2#12+3#1−1&,2]Root[#13−2#12+3#1−1&,3]2+(56108x3−81399)Root[#13−2#12+3#1−1&,1]2Root[#13−2#12+3#1−1&,3]2+(2142x3+79343)Root[#13−2#12+3#1−1&,1]Root[#13−2#12+3#1−1&,3]2+(7942x3+85)Root[#13−2#12+3#1−1&,3]−2(46379x3+51546)Root[#13−2#12+3#1−1&,3]+2(115687x3−67461)Root[#13−2#12+3#1−1&,2]2Root[#13−2#12+3#1−1&,3]+(444852x3−486021)Root[#13−2#12+3#1−1&,2]Root[#13−2#12+3#1−1&,3]−8(2080x3−3773)Root[#13−2#12+3#1−1&,1]2Root[#13−2#12+3#1−1&,3]+(551538x3−557355)Root[#13−2#12+3#1−1&,1]Root[#13−2#12+3#1−1&,3]+(59119−91060x3)Root[#13−2#12+3#1−1&,2]2+2(101430x3−63701)Root[#13−2#12+3#1−1&,1]Root[#13−2#12+3#1−1&,2]2+2(187565−285533x3)Root[#13−2#12+3#1−1&,2]+1087(36x3−25)Root[#13−2#12+3#1−1&,2]+665867−605784x3Root[#13−2#12+3#1−1&,2]+469041−364360x3Root[#13−2#12+3#1−1&,1]−51016Root[#13−2#12+3#1−1&,1]Root[#13−2#12+3#1−1&,2](2−5Root[#13−2#12+3#1−1&,1]+Root[#13−2#12+3#1−1&,1]2)(Root[#13−2#12+3#1−1&,1]−Root[#13−2#12+3#1−1&,2])(−3+Root[#13−2#12+3#1−1&,2])Root[#13−2#12+3#1−1&,2]2(Root[#13−2#12+3#1−1&,1]−Root[#13−2#12+3#1−1&,3])(Root[#13−2#12+3#1−1&,2]−Root[#13−2#12+3#1−1&,3])(−3+Root[#13−2#12+3#1−1&,3])Root[#13−2#12+3#1−1&,3]2(−2+Root[#13−2#12+3#1−1&,2]+Root[#13−2#12+3#1−1&,3])2(1+Root[#13−2#12+3#1−1&,2]+Root[#13−2#12+3#1−1&,3])(−3+Root[#13−2#12+3#1−1&,2]2+2Root[#13−2#12+3#1−1&,1]Root[#13−2#12+3#1−1&,3])}}

✓ Maple : cpu = 0.519 (sec), leaf count = 866

{y(x)=−∫−(x(11−369)(44+1269)231200+44+1269312+23)244+12693(36944+12693−1144+12693+100)(−ln⁡(x)+2x3)32313800x3((cos⁡(344+12693(36944+12693−1144+12693+100)ln⁡(x)1200))2+(sin⁡(344+12693(36944+12693−1144+12693+100)ln⁡(x)1200))2)dxx(−11+369)(44+1269)23600−44+126936+23+(∫−x(−11+369)(44+1269)23600−44+126936+23x(11−369)(44+1269)231200+44+1269312+2344+12693232300x3((1003+(69−113)44+12693)3cos⁡(344+12693(36944+12693−1144+12693+100)ln⁡(x)1200)−3sin⁡(344+12693(36944+12693−1144+12693+100)ln⁡(x)1200)(−1003+(69−11/3)44+12693))(x3−ln⁡(x)2)dx+_C2)x(11−369)(44+1269)231200+44+1269312+23cos⁡(344+12693(36944+12693−1144+12693+100)ln⁡(x)1200)+(∫−3x(−11+369)(44+1269)2/3600−1/644+12693+2/3x(11−369)(44+1269)2/31200+1/1244+12693+2/344+12693232300x3((−1003+(69−113)44+12693)cos⁡(344+12693(36944+12693−1144+12693+100)ln⁡(x)1200)+(1003+(69−113)44+12693)33sin⁡(344+12693(36944+12693−1144+12693+100)ln⁡(x)1200))(x3−ln⁡(x)2)dx+_C3)x(11−369)(44+1269)231200+44+1269312+23sin⁡(344+12693(36944+12693−1144+12693+100)ln⁡(x)1200)+_C1x(−11+369)(44+1269)23600−44+126936+23}

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