#### 2.46   ODE No. 46

$-x^{-a} y(x)-x^a y(x)^3+a x^{-a-1}-x^{-2 a}+y'(x)+3 y(x)^2=0$ Mathematica : cpu = 0.281457 (sec), leaf count = 228

$\left \{\left \{y(x)\to x^{-a}-\frac {e^{-\frac {2 x^{1-a}}{1-a}}}{\sqrt {-\frac {2^{\frac {2 (a+1)}{a-1}+1} x^{a+1} \left (\frac {x^{1-a}}{1-a}\right )^{\frac {a+1}{a-1}} \Gamma \left (\frac {a+1}{1-a},-\frac {4 x^{1-a}}{a-1}\right )}{a-1}+c_1}}\right \},\left \{y(x)\to x^{-a}+\frac {e^{-\frac {2 x^{1-a}}{1-a}}}{\sqrt {-\frac {2^{\frac {2 (a+1)}{a-1}+1} x^{a+1} \left (\frac {x^{1-a}}{1-a}\right )^{\frac {a+1}{a-1}} \Gamma \left (\frac {a+1}{1-a},-\frac {4 x^{1-a}}{a-1}\right )}{a-1}+c_1}}\right \}\right \}$ Maple : cpu = 0.085 (sec), leaf count = 956

$\left \{ y \left ( x \right ) =-{{{\rm e}^{2\,{\frac {x}{ \left ( a-1 \right ) {x}^{a}}}}}{\frac {1}{\sqrt {{\it \_C1}-2\,{\frac {1}{1-a}{2}^{-2\,{\frac {a}{1-a}}-2\, \left ( 1-a \right ) ^{-1}} \left ( \left ( 1-a \right ) ^{-1} \right ) ^{-{\frac {a}{1-a}}- \left ( 1-a \right ) ^{-1}} \left ( -{\frac { \left ( a-1 \right ) \left ( 1-a \right ) }{ \left ( a+1 \right ) \left ( -3+a \right ) }{2}^{-3+2\,{\frac {a}{1-a}}+2\, \left ( 1-a \right ) ^{-1}+2\, \left ( a-1 \right ) ^{-1}}{x}^{-{\frac {{a}^{2}}{1-a}}+ \left ( 1-a \right ) ^{-1}-1+a} \left ( \left ( 1-a \right ) ^{-1} \right ) ^{{\frac {a}{1-a}}+ \left ( 1-a \right ) ^{-1}} \left ( -4\,{\frac {{x}^{1-a}{a}^{2}}{1-a}}+8\,{\frac {a{x}^{1-a}}{1-a}}-4\,{\frac {{x}^{1-a}}{1-a}}+2\,a-2 \right ) \left ( {\frac {{x}^{1-a}}{1-a}} \right ) ^{ \left ( a-1 \right ) ^{-1}}{{\rm e}^{2\,{\frac {{x}^{1-a}}{a-1}}}}{{\sl M}_{-{\frac {a}{a-1}},\,- \left ( a-1 \right ) ^{-1}+1/2}\left (-4\,{\frac {{x}^{1-a}}{a-1}}\right )}}+{\frac { \left ( a-1 \right ) \left ( 1-a \right ) }{ \left ( a+1 \right ) \left ( -3+a \right ) }{2}^{-1+2\,{\frac {a}{1-a}}+2\, \left ( 1-a \right ) ^{-1}+2\, \left ( a-1 \right ) ^{-1}}{x}^{-{\frac {{a}^{2}}{1-a}}+ \left ( 1-a \right ) ^{-1}-1+a} \left ( \left ( 1-a \right ) ^{-1} \right ) ^{{\frac {a}{1-a}}+ \left ( 1-a \right ) ^{-1}} \left ( {\frac {{x}^{1-a}}{1-a}} \right ) ^{ \left ( a-1 \right ) ^{-1}}{{\rm e}^{2\,{\frac {{x}^{1-a}}{a-1}}}}{{\sl M}_{- \left ( a-1 \right ) ^{-1},\,- \left ( a-1 \right ) ^{-1}+1/2}\left (-4\,{\frac {{x}^{1-a}}{a-1}}\right )}} \right ) }}}}}+ \left ( {x}^{a} \right ) ^{-1},y \left ( x \right ) ={{{\rm e}^{2\,{\frac {x}{ \left ( a-1 \right ) {x}^{a}}}}}{\frac {1}{\sqrt {{\it \_C1}-2\,{\frac {1}{1-a}{2}^{-2\,{\frac {a}{1-a}}-2\, \left ( 1-a \right ) ^{-1}} \left ( \left ( 1-a \right ) ^{-1} \right ) ^{-{\frac {a}{1-a}}- \left ( 1-a \right ) ^{-1}} \left ( -{\frac { \left ( a-1 \right ) \left ( 1-a \right ) }{ \left ( a+1 \right ) \left ( -3+a \right ) }{2}^{-3+2\,{\frac {a}{1-a}}+2\, \left ( 1-a \right ) ^{-1}+2\, \left ( a-1 \right ) ^{-1}}{x}^{-{\frac {{a}^{2}}{1-a}}+ \left ( 1-a \right ) ^{-1}-1+a} \left ( \left ( 1-a \right ) ^{-1} \right ) ^{{\frac {a}{1-a}}+ \left ( 1-a \right ) ^{-1}} \left ( -4\,{\frac {{x}^{1-a}{a}^{2}}{1-a}}+8\,{\frac {a{x}^{1-a}}{1-a}}-4\,{\frac {{x}^{1-a}}{1-a}}+2\,a-2 \right ) \left ( {\frac {{x}^{1-a}}{1-a}} \right ) ^{ \left ( a-1 \right ) ^{-1}}{{\rm e}^{2\,{\frac {{x}^{1-a}}{a-1}}}}{{\sl M}_{-{\frac {a}{a-1}},\,- \left ( a-1 \right ) ^{-1}+1/2}\left (-4\,{\frac {{x}^{1-a}}{a-1}}\right )}}+{\frac { \left ( a-1 \right ) \left ( 1-a \right ) }{ \left ( a+1 \right ) \left ( -3+a \right ) }{2}^{-1+2\,{\frac {a}{1-a}}+2\, \left ( 1-a \right ) ^{-1}+2\, \left ( a-1 \right ) ^{-1}}{x}^{-{\frac {{a}^{2}}{1-a}}+ \left ( 1-a \right ) ^{-1}-1+a} \left ( \left ( 1-a \right ) ^{-1} \right ) ^{{\frac {a}{1-a}}+ \left ( 1-a \right ) ^{-1}} \left ( {\frac {{x}^{1-a}}{1-a}} \right ) ^{ \left ( a-1 \right ) ^{-1}}{{\rm e}^{2\,{\frac {{x}^{1-a}}{a-1}}}}{{\sl M}_{- \left ( a-1 \right ) ^{-1},\,- \left ( a-1 \right ) ^{-1}+1/2}\left (-4\,{\frac {{x}^{1-a}}{a-1}}\right )}} \right ) }}}}}+ \left ( {x}^{a} \right ) ^{-1} \right \}$