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8.13   ODE No. 1603

d2dx2y(x)−(a(y(x))2+bxy(x)+cx2+αy(x)+βx+γ)−32=0

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

Mathematica: cpu = 60.655702 (sec), leaf count = 42 DSolve[y″(x)−1(ay(x)2+bxy(x)+cx2+dy(x)+ex+k)3/2=0,y(x),x]

Maple: cpu = 59.530 (sec), leaf count = 13291 {y(x)=12a(2RootOf(−4arctan⁡(1/24acx−b2x+2aβ−αba(−aβ2+4acγ−cα2+bβα−γb2))ac+arctan⁡(1/24acx−b2x+2aβ−αba(−aβ2+4acγ−cα2+bβα−γb2))b2−2∫_Z(16a2c2−8ab2c+b4)−116a2c2−8ab2c+b4(64a3γ2c_g2−16a2γ2b2_g2−16a3β2_g2γ+64a3γc2_g2+4aγb4_g2+16βbαa2_g2c+16βbαa2_g2γ−32a2γc_g2αb+64a3γc_g2β−32a2γc_g2α2−16a2γb2_g2β−32a2γc_g2b2+4aγb2_g2α2+8aγb3_g2α+_C1b6+4a2β2_g2b2−16α2a2c2_g2+4α4ac_g2−16a3β2_g2c+4a2β2_g2α2−64γ_C1a3c2−4γ_C1ab4−64_C1a3c3+_C1α2b4+2_C1αb5−64_C1a3βc2+16_C1a2α2c2+48_C1a2b2c2−4_C1ab4β−12_C1ab4c−1024γ4aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4c2−64γ4aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4−10244aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4βc2+2564aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3α2c2+7684aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2c2−644aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4β−1924aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4c+164aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gaα2b4+324aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gaαb5+512γ4aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2c+5124aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3αbc2+5124aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2βc−1284aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2α2b2c−2564aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2αb3c−10244aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4c3+164aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gab6+32_C1a2αbc2+32_C1a2b2βc−8_C1aα2b2c−16_C1aαb3c+32γ_C1a2b2c−16a3β3_g2−4βbα3a_g2−8βb2α2a_g2−4βb3αa_g2+24a2β2_g2αb−16α2a2c_g2β+8α3ac_g2b+4α2ac_g2b2)(−1024γ∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4c2+512γ∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2c−64γ∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4−1024∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4βc2−1024∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4c3+256∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3α2c2+512∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3αbc2+512∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2βc+768∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2c2−128∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2α2b2c−256∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2αb3c−64∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4β−192∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4c+16∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gaα2b4+32∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gaαb5+16∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gab6+16a2γc4aβ+4ac+4aγ−α2−2αb−b2_g2−4aγb24aβ+4ac+4aγ−α2−2αb−b2_g2−4a2β24aβ+4ac+4aγ−α2−2αb−b2_g2−4α2ac4aβ+4ac+4aγ−α2−2αb−b2_g2+4βbαa4aβ+4ac+4aγ−α2−2αb−b2_g2−164aβ+4ac+4aγ−α2−2αb−b2_C1a2c2+84aβ+4ac+4aγ−α2−2αb−b2_C1ab2c−4aβ+4ac+4aγ−α2−2αb−b2_C1b4)−1d_ga(−aβ2+4acγ−cα2+bβα−γb2)+2_C2a(−aβ2+4acγ−cα2+bβα−γb2))a4ax2c−b2x2+4aβx−2αbx+4aγ−α2−bx−α),y(x)=12a(2RootOf(−4arctan⁡(1/24acx−b2x+2aβ−αba(−aβ2+4acγ−cα2+bβα−γb2))ac+arctan⁡(1/24acx−b2x+2aβ−αba(−aβ2+4acγ−cα2+bβα−γb2))b2+2∫_Z(16a2c2−8ab2c+b4)−116a2c2−8ab2c+b4(64a3γ2c_g2−16a2γ2b2_g2−16a3β2_g2γ+64a3γc2_g2+4aγb4_g2+16βbαa2_g2c+16βbαa2_g2γ−32a2γc_g2αb+64a3γc_g2β−32a2γc_g2α2−16a2γb2_g2β−32a2γc_g2b2+4aγb2_g2α2+8aγb3_g2α+_C1b6+4a2β2_g2b2−16α2a2c2_g2+4α4ac_g2−16a3β2_g2c+4a2β2_g2α2−64γ_C1a3c2−4γ_C1ab4−64_C1a3c3+_C1α2b4+2_C1αb5−64_C1a3βc2+16_C1a2α2c2+48_C1a2b2c2−4_C1ab4β−12_C1ab4c−1024γ4aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4c2−64γ4aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4−10244aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4βc2+2564aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3α2c2+7684aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2c2−644aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4β−1924aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4c+164aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gaα2b4+324aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gaαb5+512γ4aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2c+5124aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3αbc2+5124aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2βc−1284aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2α2b2c−2564aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2αb3c−10244aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4c3+164aβ+4ac+4aγ−α2−2αb−b2∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gab6+32_C1a2αbc2+32_C1a2b2βc−8_C1aα2b2c−16_C1aαb3c+32γ_C1a2b2c−16a3β3_g2−4βbα3a_g2−8βb2α2a_g2−4βb3αa_g2+24a2β2_g2αb−16α2a2c_g2β+8α3ac_g2b+4α2ac_g2b2)(−1024γ∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4c2+512γ∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2c−64γ∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4−1024∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4βc2−1024∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga4c3+256∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3α2c2+512∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3αbc2+512∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2βc+768∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga3b2c2−128∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2α2b2c−256∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2αb3c−64∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4β−192∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_ga2b4c+16∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gaα2b4+32∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gaαb5+16∫164_g2a4c2−32_g2a3b2c+4_g2a2b4+16a2c2−8ab2c+b4116a3_g2β+16a3_g2c+16_g2a3γ−4a2_g2α2−8a2_g2αb−4a2_g2b2+4aβ+4ac+4aγ−α2−2αb−b2ad_gab6+16a2γc4aβ+4ac+4aγ−α2−2αb−b2_g2−4aγb24aβ+4ac+4aγ−α2−2αb−b2_g2−4a2β24aβ+4ac+4aγ−α2−2αb−b2_g2−4α2ac4aβ+4ac+4aγ−α2−2αb−b2_g2+4βbαa4aβ+4ac+4aγ−α2−2αb−b2_g2−164aβ+4ac+4aγ−α2−2αb−b2_C1a2c2+84aβ+4ac+4aγ−α2−2αb−b2_C1ab2c−4aβ+4ac+4aγ−α2−2αb−b2_C1b4)−1d_ga(−aβ2+4acγ−cα2+bβα−γb2)+2_C2a(−aβ2+4acγ−cα2+bβα−γb2))a4ax2c−b2x2+4aβx−2αbx+4aγ−α2−bx−α)}

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