4.303   ODE No. 1303

(ax2+bx+c)d2dx2y(x)+(dx+f)ddxy(x)+gy(x)=0

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

Mathematica: cpu = 14.510843 (sec), leaf count = 56 \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{g \unicode {f818}(\unicode {f817})+(\unicode {f817} d+f) \unicode {f818}'(\unicode {f817})+\left (a \unicode {f817}^2+b \unicode {f817}+c\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2\right \}\right )(x)\right \}\right \}

Maple: cpu = 0.140 (sec), leaf count = 501 {y(x)=_C12F1(12a(a+d+a2+(2d4g)a+d2),12a(ad+a2+(2d4g)a+d2);12a2(d4ac+b2a2a2af+bd)14ac+b2a2;18ac2b2((2a2xab)4ac+b2a2+4acb2))+_C2(24ac+b2a2xa2+4ac+b2a2ba4ac+b2)1a2(a(ad2)4ac+b2a2+afbd2)14ac+b2a22F1(12a2(a(a+a2+(2d4g)a+d2)4ac+b2a2+2afbd)14ac+b2a2,12a2(a(aa2+(2d4g)a+d2)4ac+b2a2+2afbd)14ac+b2a2;12a2(4a24ac+b2a2d4ac+b2a2a+2afbd)14ac+b2a2;18ac2b2((2a2xab)4ac+b2a2+4acb2))}