\[ y''(x)=-y'(x) \left (\frac {\text {b1} (-\text {al1}-\text {bl1}+1)}{\text {b1} x-\text {a1}}+\frac {\text {b2} (-\text {al2}-\text {bl2}+1)}{\text {b2} x-\text {a2}}+\frac {\text {b3} (-\text {al3}-\text {bl3}+1)}{\text {b3} x-\text {a3}}\right )-\frac {y(x) \left (\frac {\text {al1} \text {bl1} (\text {a1} \text {b2}-\text {a2} \text {b1}) (\text {a3} \text {b1}-\text {a1} \text {b3})}{\text {b1} x-\text {a1}}+\frac {\text {al2} \text {bl2} (\text {a1} \text {b2}-\text {a2} \text {b1}) (\text {a2} \text {b3}-\text {a3} \text {b2})}{\text {b2} x-\text {a2}}+\frac {\text {al3} \text {bl3} (\text {a3} \text {b1}-\text {a1} \text {b3}) (\text {a2} \text {b3}-\text {a3} \text {b2})}{\text {b3} x-\text {a3}}\right )}{(\text {b1} x-\text {a1}) (\text {b2} x-\text {a2}) (\text {b3} x-\text {a3})} \] ✗ Mathematica : cpu = 202.059 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\text {a1}-\unicode {f817} \text {b1})^2 (\text {a2}-\unicode {f817} \text {b2})^2 \unicode {f818}''(\unicode {f817}) (\text {a3}-\unicode {f817} \text {b3})^2+(\text {a1}-\unicode {f817} \text {b1}) (\text {a2}-\unicode {f817} \text {b2}) \left (\text {al1} \text {b1} \text {b2} \text {b3} \unicode {f817}^2+\text {al2} \text {b1} \text {b2} \text {b3} \unicode {f817}^2+\text {al3} \text {b1} \text {b2} \text {b3} \unicode {f817}^2-3 \text {b1} \text {b2} \text {b3} \unicode {f817}^2+\text {b1} \text {b2} \text {b3} \text {bl1} \unicode {f817}^2+\text {b1} \text {b2} \text {b3} \text {bl2} \unicode {f817}^2+\text {b1} \text {b2} \text {b3} \text {bl3} \unicode {f817}^2+2 \text {a3} \text {b1} \text {b2} \unicode {f817}-\text {a3} \text {al1} \text {b1} \text {b2} \unicode {f817}-\text {a3} \text {al2} \text {b1} \text {b2} \unicode {f817}+2 \text {a2} \text {b1} \text {b3} \unicode {f817}-\text {a2} \text {al1} \text {b1} \text {b3} \unicode {f817}-\text {a2} \text {al3} \text {b1} \text {b3} \unicode {f817}+2 \text {a1} \text {b2} \text {b3} \unicode {f817}-\text {a1} \text {al2} \text {b2} \text {b3} \unicode {f817}-\text {a1} \text {al3} \text {b2} \text {b3} \unicode {f817}-\text {a3} \text {b1} \text {b2} \text {bl1} \unicode {f817}-\text {a2} \text {b1} \text {b3} \text {bl1} \unicode {f817}-\text {a3} \text {b1} \text {b2} \text {bl2} \unicode {f817}-\text {a1} \text {b2} \text {b3} \text {bl2} \unicode {f817}-\text {a2} \text {b1} \text {b3} \text {bl3} \unicode {f817}-\text {a1} \text {b2} \text {b3} \text {bl3} \unicode {f817}-\text {a2} \text {a3} \text {b1}+\text {a2} \text {a3} \text {al1} \text {b1}-\text {a1} \text {a3} \text {b2}+\text {a1} \text {a3} \text {al2} \text {b2}-\text {a1} \text {a2} \text {b3}+\text {a1} \text {a2} \text {al3} \text {b3}+\text {a2} \text {a3} \text {b1} \text {bl1}+\text {a1} \text {a3} \text {b2} \text {bl2}+\text {a1} \text {a2} \text {b3} \text {bl3}\right ) \unicode {f818}'(\unicode {f817}) (\text {a3}-\unicode {f817} \text {b3})+\left (-\unicode {f817}^2 \text {al1} \text {b2}^2 \text {b3}^2 \text {bl1} \text {a1}^2+\unicode {f817} \text {a2} \text {al1} \text {b2} \text {b3}^2 \text {bl1} \text {a1}^2+\unicode {f817} \text {a3} \text {al1} \text {b2}^2 \text {b3} \text {bl1} \text {a1}^2-\text {a2} \text {a3} \text {al1} \text {b2} \text {b3} \text {bl1} \text {a1}^2-\text {a3}^2 \text {al2} \text {b2}^2 \text {bl2} \text {a1}^2-\unicode {f817} \text {a2} \text {al2} \text {b2} \text {b3}^2 \text {bl2} \text {a1}^2+\unicode {f817} \text {a3} \text {al2} \text {b2}^2 \text {b3} \text {bl2} \text {a1}^2+\text {a2} \text {a3} \text {al2} \text {b2} \text {b3} \text {bl2} \text {a1}^2-\text {a2}^2 \text {al3} \text {b3}^2 \text {bl3} \text {a1}^2+\unicode {f817} \text {a2} \text {al3} \text {b2} \text {b3}^2 \text {bl3} \text {a1}^2-\unicode {f817} \text {a3} \text {al3} \text {b2}^2 \text {b3} \text {bl3} \text {a1}^2+\text {a2} \text {a3} \text {al3} \text {b2} \text {b3} \text {bl3} \text {a1}^2-\unicode {f817} \text {a3}^2 \text {al1} \text {b1} \text {b2}^2 \text {bl1} \text {a1}-\unicode {f817} \text {a2}^2 \text {al1} \text {b1} \text {b3}^2 \text {bl1} \text {a1}+\unicode {f817}^2 \text {a2} \text {al1} \text {b1} \text {b2} \text {b3}^2 \text {bl1} \text {a1}+\text {a2} \text {a3}^2 \text {al1} \text {b1} \text {b2} \text {bl1} \text {a1}+\unicode {f817}^2 \text {a3} \text {al1} \text {b1} \text {b2}^2 \text {b3} \text {bl1} \text {a1}+\text {a2}^2 \text {a3} \text {al1} \text {b1} \text {b3} \text {bl1} \text {a1}-2 \unicode {f817} \text {a2} \text {a3} \text {al1} \text {b1} \text {b2} \text {b3} \text {bl1} \text {a1}+\unicode {f817} \text {a3}^2 \text {al2} \text {b1} \text {b2}^2 \text {bl2} \text {a1}+\unicode {f817} \text {a2}^2 \text {al2} \text {b1} \text {b3}^2 \text {bl2} \text {a1}+\unicode {f817}^2 \text {a2} \text {al2} \text {b1} \text {b2} \text {b3}^2 \text {bl2} \text {a1}+\text {a2} \text {a3}^2 \text {al2} \text {b1} \text {b2} \text {bl2} \text {a1}-\unicode {f817}^2 \text {a3} \text {al2} \text {b1} \text {b2}^2 \text {b3} \text {bl2} \text {a1}-\text {a2}^2 \text {a3} \text {al2} \text {b1} \text {b3} \text {bl2} \text {a1}-2 \unicode {f817} \text {a2} \text {a3} \text {al2} \text {b1} \text {b2} \text {b3} \text {bl2} \text {a1}+\unicode {f817} \text {a3}^2 \text {al3} \text {b1} \text {b2}^2 \text {bl3} \text {a1}+\unicode {f817} \text {a2}^2 \text {al3} \text {b1} \text {b3}^2 \text {bl3} \text {a1}-\unicode {f817}^2 \text {a2} \text {al3} \text {b1} \text {b2} \text {b3}^2 \text {bl3} \text {a1}-\text {a2} \text {a3}^2 \text {al3} \text {b1} \text {b2} \text {bl3} \text {a1}+\unicode {f817}^2 \text {a3} \text {al3} \text {b1} \text {b2}^2 \text {b3} \text {bl3} \text {a1}+\text {a2}^2 \text {a3} \text {al3} \text {b1} \text {b3} \text {bl3} \text {a1}-2 \unicode {f817} \text {a2} \text {a3} \text {al3} \text {b1} \text {b2} \text {b3} \text {bl3} \text {a1}-\text {a2}^2 \text {a3}^2 \text {al1} \text {b1}^2 \text {bl1}+\unicode {f817} \text {a2} \text {a3}^2 \text {al1} \text {b1}^2 \text {b2} \text {bl1}+\unicode {f817} \text {a2}^2 \text {a3} \text {al1} \text {b1}^2 \text {b3} \text {bl1}-\unicode {f817}^2 \text {a2} \text {a3} \text {al1} \text {b1}^2 \text {b2} \text {b3} \text {bl1}-\unicode {f817}^2 \text {a2}^2 \text {al2} \text {b1}^2 \text {b3}^2 \text {bl2}-\unicode {f817} \text {a2} \text {a3}^2 \text {al2} \text {b1}^2 \text {b2} \text {bl2}+\unicode {f817} \text {a2}^2 \text {a3} \text {al2} \text {b1}^2 \text {b3} \text {bl2}+\unicode {f817}^2 \text {a2} \text {a3} \text {al2} \text {b1}^2 \text {b2} \text {b3} \text {bl2}-\unicode {f817}^2 \text {a3}^2 \text {al3} \text {b1}^2 \text {b2}^2 \text {bl3}+\unicode {f817} \text {a2} \text {a3}^2 \text {al3} \text {b1}^2 \text {b2} \text {bl3}-\unicode {f817} \text {a2}^2 \text {a3} \text {al3} \text {b1}^2 \text {b3} \text {bl3}+\unicode {f817}^2 \text {a2} \text {a3} \text {al3} \text {b1}^2 \text {b2} \text {b3} \text {bl3}\right ) \unicode {f818}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 3.998 (sec), leaf count = 2603
\[ \left \{ y \left ( x \right ) = \left ( {\it b3}\,x-{\it a3} \right ) ^{{\frac {1}{2} \left ( \left ( {\it al3}+{\it bl3} \right ) \sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}+ \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) \sqrt {{{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2}}+{{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) {\frac {1}{\sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}}}}} \left ( {\it b2}\,x-{\it a2} \right ) ^{{\frac {{\it al2}}{2}}+{\frac {{\it bl2}}{2}}+{\frac {1}{2}\sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}}}} \left ( {\it HeunG} \left ( {\frac {{\it b2}\, \left ( {\it a1}\,{\it b3}-{\it a3}\,{\it b1} \right ) }{{\it b3}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) }},-{\frac {1}{4\,{\it b3}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) } \left ( \left ( \left ( 2\,{\it b2}\, \left ( {\it a1}\,{\it b3}-{\it a3}\,{\it b1} \right ) \sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}}+ \left ( 4\,{\it a1}\,{\it b3}-2\,{\it a3}\,{\it b1} \right ) {\it b2}-2\,{\it a2}\,{\it b1}\,{\it b3} \right ) \sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}-2\,{\it b2}\, \left ( {\it a1}\,{\it b3}-{\it a3}\,{\it b1} \right ) \sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}}+ \left ( 2\,{\it a1}\, \left ( \left ( -4\,{\it bl1}+{\it bl2}+{\it bl3}+{\it al2}+{\it al3}-2 \right ) {\it al1}+ \left ( {\it bl2}+{\it bl3}+{\it al2}+{\it al3}-2 \right ) {\it bl1}-{\it bl2}-{\it bl3}-{\it al2}-{\it al3} \right ) {\it b3}-2\, \left ( \left ( -2\,{\it bl1}+{\it bl2}+{\it al2}-1 \right ) {\it al1}+ \left ( -1+{\it al2}+{\it bl2} \right ) {\it bl1}+2\,{\it al3}\,{\it bl3}+ \left ( -2\,{\it bl2}-1 \right ) {\it al2}-{\it bl2} \right ) {\it b1}\,{\it a3} \right ) {\it b2}-2\,{\it b1}\, \left ( \left ( -2\,{\it bl1}+{\it bl3}+{\it al3}-1 \right ) {\it al1}+ \left ( -1+{\it al3}+{\it bl3} \right ) {\it bl1}+ \left ( -2\,{\it bl3}-1 \right ) {\it al3}+2\,{\it al2}\,{\it bl2}-{\it bl3} \right ) {\it a2}\,{\it b3} \right ) \sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}+ \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) \left ( \left ( 2\,\sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}-2 \right ) \sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}- \left ( {{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2} \right ) ^{{\frac {3}{2}}}+ \left ( {{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+2\,{{\it al3}}^{2}+12\,{\it al3}\,{\it bl3}+{{\it bl1}}^{2}+2\,{{\it bl3}}^{2} \right ) \sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}-2\,{{\it bl3}}^{2}-12\,{\it al3}\,{\it bl3}-2\,{{\it al3}}^{2} \right ) {\it b3} \right ) {\frac {1}{\sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}}}},1+{\frac {1}{2}\sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}}}-{\frac {1}{2}\sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}}+{\frac {1}{2}\sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}},-{\frac {1}{2} \left ( \left ( \sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}-\sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}}-2 \right ) \sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}+ \left ( 2\,{\it al1}+2\,{\it al2}-4\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}-4 \right ) {\it bl3}+ \left ( {\it al1}+{\it al2}+{\it bl1}+{\it bl2}-2 \right ) \left ( {\it al1}+{\it al2}+2\,{\it al3}+{\it bl1}+{\it bl2}-2 \right ) \right ) {\frac {1}{\sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}}}},1-\sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}},1+\sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}},{\frac {{\it b2}\, \left ( -{\it b1}\,x+{\it a1} \right ) }{{\it a1}\,{\it b2}-{\it a2}\,{\it b1}}} \right ) \left ( {\it b1}\,x-{\it a1} \right ) ^{{\frac {{\it al1}}{2}}+{\frac {{\it bl1}}{2}}-{\frac {1}{2}\sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}}}{\it \_C1}+{\it HeunG} \left ( {\frac {{\it b2}\, \left ( {\it a1}\,{\it b3}-{\it a3}\,{\it b1} \right ) }{{\it b3}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) }},{\frac {1}{4\,{\it b3}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) } \left ( - \left ( -2\, \left ( \sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}}{\it a1}\,{\it b2}\,{\it b3}-\sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}}{\it a3}\,{\it b1}\,{\it b2}+2\,{\it a1}\,{\it b2}\,{\it b3}-{\it a2}\,{\it b1}\,{\it b3}-{\it a3}\,{\it b1}\,{\it b2} \right ) \sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}-2\,{\it b2}\, \left ( {\it a1}\,{\it b3}-{\it a3}\,{\it b1} \right ) \sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}}+ \left ( 2\,{\it a1}\, \left ( \left ( -4\,{\it bl1}+{\it bl2}+{\it bl3}+{\it al2}+{\it al3}-2 \right ) {\it al1}+ \left ( {\it bl2}+{\it bl3}+{\it al2}+{\it al3}-2 \right ) {\it bl1}-{\it bl2}-{\it bl3}-{\it al2}-{\it al3} \right ) {\it b2}-2\,{\it b1}\, \left ( \left ( -2\,{\it bl1}+{\it bl3}+{\it al3}-1 \right ) {\it al1}+ \left ( -1+{\it al3}+{\it bl3} \right ) {\it bl1}+ \left ( -2\,{\it bl3}-1 \right ) {\it al3}+2\,{\it al2}\,{\it bl2}-{\it bl3} \right ) {\it a2} \right ) {\it b3}-2\, \left ( \left ( -2\,{\it bl1}+{\it bl2}+{\it al2}-1 \right ) {\it al1}+ \left ( -1+{\it al2}+{\it bl2} \right ) {\it bl1}+2\,{\it al3}\,{\it bl3}+ \left ( -2\,{\it bl2}-1 \right ) {\it al2}-{\it bl2} \right ) {\it b1}\,{\it a3}\,{\it b2} \right ) \sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}- \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) \left ( -2\, \left ( 1+\sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}} \right ) \sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}- \left ( {{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2} \right ) ^{{\frac {3}{2}}}+ \left ( {{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}-2\,{{\it al3}}^{2}-12\,{\it al3}\,{\it bl3}+{{\it bl1}}^{2}-2\,{{\it bl3}}^{2} \right ) \sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}-2\,{{\it bl3}}^{2}-12\,{\it al3}\,{\it bl3}-2\,{{\it al3}}^{2} \right ) {\it b3} \right ) {\frac {1}{\sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}}}},1+{\frac {1}{2}\sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}}}+{\frac {1}{2}\sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}}+{\frac {1}{2}\sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}},{\frac {1}{2} \left ( \left ( 2+\sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}+\sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}} \right ) \sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}- \left ( 2\,{\it al1}+2\,{\it al2}-4\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}-4 \right ) {\it bl3}- \left ( {\it al1}+{\it al2}+{\it bl1}+{\it bl2}-2 \right ) \left ( {\it al1}+{\it al2}+2\,{\it al3}+{\it bl1}+{\it bl2}-2 \right ) \right ) {\frac {1}{\sqrt {{{\it al1}}^{2}+ \left ( 2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al1}+{{\it al2}}^{2}+ \left ( 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it al2}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it bl1}+2\,{\it bl2}+8\,{\it bl3}-4 \right ) {\it al3}+{{\it bl1}}^{2}+ \left ( 2\,{\it bl2}+2\,{\it bl3}-4 \right ) {\it bl1}+{{\it bl2}}^{2}+ \left ( 2\,{\it bl3}-4 \right ) {\it bl2}+2\,{{\it bl3}}^{2}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( {\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3}-2 \right ) ^{2}}-4\,{\it bl3}+4}}}},1+\sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}},1+\sqrt {{{\it al2}}^{2}+6\,{\it al2}\,{\it bl2}+{{\it bl2}}^{2}},{\frac {{\it b2}\, \left ( -{\it b1}\,x+{\it a1} \right ) }{{\it a1}\,{\it b2}-{\it a2}\,{\it b1}}} \right ) \left ( {\it b1}\,x-{\it a1} \right ) ^{{\frac {{\it al1}}{2}}+{\frac {{\it bl1}}{2}}+{\frac {1}{2}\sqrt {{{\it al1}}^{2}+6\,{\it al1}\,{\it bl1}+{{\it bl1}}^{2}}}}{\it \_C2} \right ) \right \} \]