\[ a y(x)^2+b x+c+y(x)^2 y'(x)^2+2 x y(x) y'(x)=0 \] ✗ Mathematica : cpu = 3600.62 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 2.361 (sec), leaf count = 5237
\[ \left \{ y \left ( x \right ) =-{\frac {1}{2\,a \left ( a+1 \right ) }\sqrt {a \left ( 16\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{5}{x}^{2}-16\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{4}bx+64\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{4}{x}^{2}+4\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{3}{b}^{2}-48\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{3}bx+96\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{3}{x}^{2}+8\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{2}{b}^{2}-48\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{2}bx+64\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{2}{x}^{2}+4\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) a{b}^{2}-16\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) abx+16\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) a{x}^{2}-4\,xb{a}^{2}-4\,{a}^{2}c-4\,abx-8\,ac-{b}^{2}-4\,c \right ) }},y \left ( x \right ) ={\frac {1}{2\,a \left ( a+1 \right ) }\sqrt {a \left ( 16\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{5}{x}^{2}-16\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{4}bx+64\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{4}{x}^{2}+4\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{3}{b}^{2}-48\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{3}bx+96\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{3}{x}^{2}+8\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{2}{b}^{2}-48\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{2}bx+64\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) {a}^{2}{x}^{2}+4\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) a{b}^{2}-16\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) abx+16\,{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!-1/4\,{\frac {b}{{\it \_a}\, \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) } \left ( 4\,{\it \_a}\,{a}^{2}+\sqrt {- \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) {{\rm e}^{4\,{\frac {a+1}{b}}}}}{{\rm e}^{-2\,{\frac {a+1}{b}}}}+8\,a{\it \_a}+4\,{\it \_a}+1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) a{x}^{2}-4\,xb{a}^{2}-4\,{a}^{2}c-4\,abx-8\,ac-{b}^{2}-4\,c \right ) }} \right \} \]