#### 2.268   ODE No. 268

$f(x) y(x) y'(x)+g(x) y(x)^2+h(x)=0$ Mathematica : cpu = 0.156886 (sec), leaf count = 146

$\left \{\left \{y(x)\to -\exp \left (\int _1^x-\frac {g(K[1])}{f(K[1])}dK[1]\right ) \sqrt {2 \int _1^x-\frac {\exp \left (-2 \int _1^{K[2]}-\frac {g(K[1])}{f(K[1])}dK[1]\right ) h(K[2])}{f(K[2])}dK[2]+c_1}\right \},\left \{y(x)\to \exp \left (\int _1^x-\frac {g(K[1])}{f(K[1])}dK[1]\right ) \sqrt {2 \int _1^x-\frac {\exp \left (-2 \int _1^{K[2]}-\frac {g(K[1])}{f(K[1])}dK[1]\right ) h(K[2])}{f(K[2])}dK[2]+c_1}\right \}\right \}$ Maple : cpu = 0.053 (sec), leaf count = 118

$\left \{ y \left ( x \right ) ={\sqrt {{{\rm e}^{2\,\int \!{\frac {g \left ( x \right ) }{f \left ( x \right ) }}\,{\rm d}x}} \left ( -2\,\int \!{\frac {h \left ( x \right ) }{f \left ( x \right ) } \left ( {{\rm e}^{\int \!{\frac {g \left ( x \right ) }{f \left ( x \right ) }}\,{\rm d}x}} \right ) ^{2}}\,{\rm d}x+{\it \_C1} \right ) } \left ( {{\rm e}^{2\,\int \!{\frac {g \left ( x \right ) }{f \left ( x \right ) }}\,{\rm d}x}} \right ) ^{-1}},y \left ( x \right ) =-{\sqrt {{{\rm e}^{2\,\int \!{\frac {g \left ( x \right ) }{f \left ( x \right ) }}\,{\rm d}x}} \left ( -2\,\int \!{\frac {h \left ( x \right ) }{f \left ( x \right ) } \left ( {{\rm e}^{\int \!{\frac {g \left ( x \right ) }{f \left ( x \right ) }}\,{\rm d}x}} \right ) ^{2}}\,{\rm d}x+{\it \_C1} \right ) } \left ( {{\rm e}^{2\,\int \!{\frac {g \left ( x \right ) }{f \left ( x \right ) }}\,{\rm d}x}} \right ) ^{-1}} \right \}$