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2.1330   ODE No. 1330

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

y″(x)=−y′(x)(Ax2+Bx+C)(x−a)(x−b)(x−c)−(DDx+e)y(x)(x−a)(x−b)(x−c) ✗ Mathematica : cpu = 178.434 (sec), leaf count = 0 , DifferentialRoot result

\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\unicode {f817} \text {DD}+e) \unicode {f818}(\unicode {f817})+\left (A \unicode {f817}^2+B \unicode {f817}+C\right ) \unicode {f818}'(\unicode {f817})-(a-\unicode {f817}) (b-\unicode {f817}) (c-\unicode {f817}) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2\right \}\right )(x)\right \}\right \}

✓ Maple : cpu = 1.19 (sec), leaf count = 1147

{y(x)=_C1HeunG(a−ca−b,DDa+Ea−b,A2−12+12A2−2A−4DD+1,1((A(b−c)a−Abc−Bc−C)A2−2A−4DD+1−(A2−A−4DD)(b−c)a+c(A2−A−4DD)b+(Bc+C)A+4c2DD−Bc−C)(2(b−c)(a−c)A2−2A−4DD+1+(−2b+2c)a+2Ac2+2Bc+2bc−2c2+2C)−1,Aa2+Ba+C(a−b)(a−c),−Ab2−Bb−C(a−b)(b−c),a−xa−b)+_C2HeunG(a−ca−b,1(a−b)3(a−c)2((a−b)(a(a−2b)A−Bb−C+(−DDa−E)b+a2DD+Ea)c2+(a3(a−2b)A2+(a(a−3b)B−2Cb−a(a−b)(a−3b))aA−B2ab−(a+b)(C−a(a−b))B−C2+(3a2−4ab+b2)C−2a(a−b)2(DDa+E))c+A2a4b+((a+b)B−ab+b2+2C)a3A+B2a3+((3a2−ab)C−a3(a−b))B+(2a−b)C2−2(a−b)(a−b/2)aC+a2(a−b)2(DDa+E)),1(2a−2c)(a−b)((a−c)(a−b)A2−2A−4DD+1+(−A+1)a2+((−b−c)A−2B−b−c)a+Abc+bc−2C),1(2a−2c)(a−b)(−(a−c)((b−c)(A−2)a2+(−2c2−Bc+(A+2)b2+2Bb+C)a+2bc2+((−A−2)b2−Bb−2C)c+Cb)A2−2A−4DD+1−(A2−3A−4DD+2)(b−c)a3+((−3A2+5A+8DD−4)c2+((A2−3A−4DD+2)b−B(1+A))c+(A2−A−4DD+2)b2+2Bb−C(A−1))a2+((−2A−4DD+2)c3+((−2A−4DD+2)b−3AB+B)c2+((−2A2+2A+8DD−4)b2−B(A+3)b−AC−2B2−3C)c−C((A−1)b+2B))a+2(A+2DD−1)bc3+((A2−A−4DD+2)b2+B(1+A)b−2C(A−1))c2+C((A−1)b−2B)c−2C2)((b−c)(a−c)A2−2A−4DD+1+(A−1)c2+(B+a+b)c−ab+C)−1,(−A+2)a2+(−B−2b−2c)a+2bc−C(a−b)(a−c),−Ab2−Bb−C(a−b)(b−c),a−xa−b)(x−a)(−A+1)a2+(−B−b−c)a+bc−C(a−b)(a−c)}

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