\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =- \left ( {\frac { \left ( 1-{\it al1}-{\it bl1} \right ) {\it b1}}{{\it b1}\,x-{\it a1}}}+{\frac { \left ( 1-{\it al2}-{\it bl2} \right ) {\it b2}}{{\it b2}\,x-{\it a2}}}+{\frac { \left ( 1-{\it al3}-{\it bl3} \right ) {\it b3}}{{\it b3}\,x-{\it a3}}} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -{\frac {y \left ( x \right ) }{ \left ( {\it b1}\,x-{\it a1} \right ) \left ( {\it b2}\,x-{\it a2} \right ) \left ( {\it b3}\,x-{\it a3} \right ) } \left ( {\frac {{\it al1}\,{\it bl1}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) \left ( -{\it a1}\,{\it b3}+{\it a3}\,{\it b1} \right ) }{{\it b1}\,x-{\it a1}}}+{\frac {{\it al2}\,{\it bl2}\, \left ( {\it a2}\,{\it b3}-{\it a3}\,{\it b2} \right ) \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) }{{\it b2}\,x-{\it a2}}}+{\frac {{\it al3}\,{\it bl3}\, \left ( -{\it a1}\,{\it b3}+{\it a3}\,{\it b1} \right ) \left ( {\it a2}\,{\it b3}-{\it a3}\,{\it b2} \right ) }{{\it b3}\,x-{\it a3}}} \right ) }=0} \]
Mathematica: cpu = 491.008850 (sec), leaf count = 842 \[ \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 = 2.074 (sec), leaf count = 2907 \[ \left \{ y \left ( x \right ) ={\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 b1}\,{\it a2} \right ) }},-{\frac {1}{4\,{\it b3}\, \left ( {\it a1}\,{\it b2}-{\it b1}\,{\it a2} \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\, \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 a1}\,{\it b3}-2\,{\it b1}\,{\it a3}\, \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 ) \right ) {\it b2}-2\,{\it b3}\,{ \it a2}\,{\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 ) \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}-4\,{\it bl3}+2\, \sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( -2+{\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+ {\it bl3} \right ) ^{2}}+4}+ \left ( {\it a1}\,{\it b2}-{\it b1}\,{\it a2} \right ) {\it b3}\, \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 ( -2+{ \it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3} \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 ) \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}-4\,{\it bl3}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( -2+{\it al1}+{\it al2}+{\it al3}+ {\it bl1}+{\it bl2}+{\it bl3} \right ) ^{2}}+4}}}},{\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}}}+1+{ \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}-4\,{\it bl3}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( -2+{\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+ {\it bl3} \right ) ^{2}}+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}-4\,{\it bl3}+2\,\sqrt { \left ( {{\it al3}} ^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( -2+{\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3} \right ) ^{2}}+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}-4\,{\it bl3}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( -2+{\it al1}+{\it al2}+{\it al3}+ {\it bl1}+{\it bl2}+{\it bl3} \right ) ^{2}}+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 b1}\,{\it a2}}} \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}}}} \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 b3}\,x-{\it a3} \right ) ^{{\frac {1}{2} \left ( \left ( { \it al3}+{\it bl3} \right ) \sqrt { \left ( 2\,{\it al1}+2\,{\it al2}+2 \,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) \sqrt {{{ \it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2}}+2\,{{\it bl3}}^ {2}+ \left ( 2\,{\it al1}+2\,{\it al2}+8\,{\it al3}+2\,{\it bl1}+2\,{ \it bl2}-4 \right ) {\it bl3}+{{\it bl2}}^{2}+ \left ( 2\,{\it al1}+2\,{ \it al2}+2\,{\it al3}+2\,{\it bl1}-4 \right ) {\it bl2}+{{\it bl1}}^{2} + \left ( 2\,{\it al1}+2\,{\it al2}+2\,{\it al3}-4 \right ) {\it bl1}+2 \,{{\it al3}}^{2}+ \left ( 2\,{\it al1}+2\,{\it al2}-4 \right ) {\it al3 }+ \left ( {\it al1}+{\it al2}-2 \right ) ^{2}}+ \left ( -2+{\it al1}+{ \it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3} \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 { \left ( 2\,{\it al1}+2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) \sqrt {{{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2}}+2\,{{\it bl3}}^{2}+ \left ( 2\,{\it al1}+2\,{\it al2}+8\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}-4 \right ) {\it bl3}+{{\it bl2}}^{2}+ \left ( 2\,{\it al1}+2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}- 4 \right ) {\it bl2}+{{\it bl1}}^{2}+ \left ( 2\,{\it al1}+2\,{\it al2}+ 2\,{\it al3}-4 \right ) {\it bl1}+2\,{{\it al3}}^{2}+ \left ( 2\,{\it al1}+2\,{\it al2}-4 \right ) {\it al3}+ \left ( {\it al1}+{\it al2}-2 \right ) ^{2}}}}}}+{\it \_C2}\,{\it HeunG} \left ( {\frac {{\it b2}\, \left ( {\it a1}\,{\it b3}-{\it a3}\,{\it b1} \right ) }{{\it b3}\, \left ( {\it a1}\,{\it b2}-{\it b1}\,{\it a2} \right ) }},{\frac {1}{4 \,{\it b3}\, \left ( {\it a1}\,{\it b2}-{\it b1}\,{\it a2} \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\, \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 a1}\,{\it b2}-2\,{\it a2}\,{\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 ) \right ) {\it b3}-2\,{\it b1}\,{\it a3}\, \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 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}-4\,{\it bl3}+2\,\sqrt { \left ( {{\it al3}} ^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( -2+{\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3} \right ) ^{2}}+4 }- \left ( {\it a1}\,{\it b2}-{\it b1}\,{\it a2} \right ) {\it b3}\, \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 ( -2+{\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3} \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 ) \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}-4\,{\it bl3}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( -2+{\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+ {\it bl3} \right ) ^{2}}+4}}}},{\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}}}+1+{\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}-4\,{\it bl3}+2\,\sqrt { \left ( {{\it al3}} ^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( -2+{\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+{\it bl3} \right ) ^{2}}+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}-4\,{\it bl3}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( -2+{\it al1}+{\it al2}+{\it al3}+ {\it bl1}+{\it bl2}+{\it bl3} \right ) ^{2}}+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}-4\,{\it bl3}+2\,\sqrt { \left ( {{\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2} \right ) \left ( -2+{\it al1}+{\it al2}+{\it al3}+{\it bl1}+{\it bl2}+ {\it bl3} \right ) ^{2}}+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 b1}\,{\it a2}}} \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}}}} \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 b3}\,x-{\it a3} \right ) ^{{\frac {1}{2} \left ( \left ( {\it al3}+{\it bl3} \right ) \sqrt { \left ( 2\,{\it al1}+2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}+2\, {\it bl2}+2\,{\it bl3}-4 \right ) \sqrt {{{\it al3}}^{2}+6\,{\it al3}\, {\it bl3}+{{\it bl3}}^{2}}+2\,{{\it bl3}}^{2}+ \left ( 2\,{\it al1}+2\, {\it al2}+8\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}-4 \right ) {\it bl3}+{ {\it bl2}}^{2}+ \left ( 2\,{\it al1}+2\,{\it al2}+2\,{\it al3}+2\,{\it bl1}-4 \right ) {\it bl2}+{{\it bl1}}^{2}+ \left ( 2\,{\it al1}+2\,{\it al2}+2\,{\it al3}-4 \right ) {\it bl1}+2\,{{\it al3}}^{2}+ \left ( 2\,{ \it al1}+2\,{\it al2}-4 \right ) {\it al3}+ \left ( {\it al1}+{\it al2}- 2 \right ) ^{2}}+ \left ( -2+{\it al1}+{\it al2}+{\it al3}+{\it bl1}+{ \it bl2}+{\it bl3} \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 { \left ( 2\,{\it al1}+2\,{\it al2}+ 2\,{\it al3}+2\,{\it bl1}+2\,{\it bl2}+2\,{\it bl3}-4 \right ) \sqrt {{ {\it al3}}^{2}+6\,{\it al3}\,{\it bl3}+{{\it bl3}}^{2}}+2\,{{\it bl3}} ^{2}+ \left ( 2\,{\it al1}+2\,{\it al2}+8\,{\it al3}+2\,{\it bl1}+2\,{ \it bl2}-4 \right ) {\it bl3}+{{\it bl2}}^{2}+ \left ( 2\,{\it al1}+2\,{ \it al2}+2\,{\it al3}+2\,{\it bl1}-4 \right ) {\it bl2}+{{\it bl1}}^{2} + \left ( 2\,{\it al1}+2\,{\it al2}+2\,{\it al3}-4 \right ) {\it bl1}+2 \,{{\it al3}}^{2}+ \left ( 2\,{\it al1}+2\,{\it al2}-4 \right ) {\it al3 }+ \left ( {\it al1}+{\it al2}-2 \right ) ^{2}}}}}} \right \} \]