#### 2.64   ODE No. 64

$y'(x)-\sqrt {\frac {a y(x)^2+b y(x)+c}{a x^2+b x+c}}=0$ Mathematica : cpu = 0.307698 (sec), leaf count = 269

$\left \{\left \{y(x)\to \frac {e^{-\sqrt {a} c_1} \left (8 a^{3/2} c e^{2 \sqrt {a} c_1} \sqrt {a x^2+b x+c}-8 a^{3/2} c \sqrt {a x^2+b x+c}+8 a^2 c x e^{2 \sqrt {a} c_1}+8 a^2 c x+2 b^3 e^{\sqrt {a} c_1}-b^3 e^{2 \sqrt {a} c_1}-2 \sqrt {a} b^2 e^{2 \sqrt {a} c_1} \sqrt {a x^2+b x+c}+2 \sqrt {a} b^2 \sqrt {a x^2+b x+c}-2 a b^2 x e^{2 \sqrt {a} c_1}-2 a b^2 x-8 a b c e^{\sqrt {a} c_1}+4 a b c e^{2 \sqrt {a} c_1}+4 a b c-b^3\right )}{a \left (16 a c-4 b^2\right )}\right \}\right \}$ Maple : cpu = 0.073 (sec), leaf count = 124

$\left \{ -{1\sqrt {{\frac {a \left ( y \left ( x \right ) \right ) ^{2}+by \left ( x \right ) +c}{a{x}^{2}+bx+c}}}\sqrt {a{x}^{2}+bx+c}\ln \left ( {\frac {1}{2} \left ( 2\,\sqrt {a{x}^{2}+bx+c}\sqrt {a}+2\,ax+b \right ) {\frac {1}{\sqrt {a}}}} \right ) {\frac {1}{\sqrt {a \left ( y \left ( x \right ) \right ) ^{2}+by \left ( x \right ) +c}}}{\frac {1}{\sqrt {a}}}}+{1\ln \left ( \sqrt {a \left ( y \left ( x \right ) \right ) ^{2}+by \left ( x \right ) +c}+{\frac {2\,ay \left ( x \right ) +b}{2}{\frac {1}{\sqrt {a}}}} \right ) {\frac {1}{\sqrt {a}}}}+{\it \_C1}=0 \right \}$