#### 2.841   ODE No. 841

$y'(x)=\frac {-2 a^{3/2} b x^2 y(x)^2+2 a^{3/2} c y(x)^2+a^{5/2} y(x)^4+\sqrt {a} b^2 x^4-2 \sqrt {a} b c x^2+\sqrt {a} c^2+b x^3}{a x^2 y(x)}$ Mathematica : cpu = 1.02406 (sec), leaf count = 236

$\left \{\left \{y(x)\to -\frac {\sqrt {4 a^3 b^2 x^3-4 a^3 b c x+2 a^{5/2} b x^2-2 a^{5/2} c+a^2 x+4 \sqrt {a} b^2 c_1 x^2-4 \sqrt {a} b c c_1+2 b c_1 x}}{\sqrt {2} \sqrt {2 a^4 b x+2 a^{3/2} b c_1+a^{7/2}}}\right \},\left \{y(x)\to \frac {\sqrt {4 a^3 b^2 x^3-4 a^3 b c x+2 a^{5/2} b x^2-2 a^{5/2} c+a^2 x+4 \sqrt {a} b^2 c_1 x^2-4 \sqrt {a} b c c_1+2 b c_1 x}}{\sqrt {2} \sqrt {2 a^4 b x+2 a^{3/2} b c_1+a^{7/2}}}\right \}\right \}$ Maple : cpu = 0.548 (sec), leaf count = 97

$\left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}\,x+1}\sqrt {{a}^{{\frac {3}{2}}} \left ( {\it \_C1}\,x+1 \right ) \left ( \left ( {\it \_C1}\,x+1 \right ) \left ( b{x}^{2}-c \right ) \sqrt {a}+{\frac {x}{2}} \right ) }{a}^{-{\frac {3}{2}}}},y \left ( x \right ) =-2\,{\frac {\sqrt {{a}^{3/2} \left ( {\it \_C1}\,x+1 \right ) \left ( \left ( {\it \_C1}\,x+1 \right ) \left ( b{x}^{2}-c \right ) \sqrt {a}+x/2 \right ) }}{{a}^{3/2} \left ( 2\,{\it \_C1}\,x+2 \right ) }} \right \}$