#### 2.494   ODE No. 494

$\left (y(x)^2-a^2 x^2\right ) y'(x)^2+\left (1-a^2\right ) x^2+2 x y(x) y'(x)=0$ Mathematica : cpu = 0.112739 (sec), leaf count = 49

$\left \{\left \{y(x)\to a c_1-\sqrt {c_1{}^2-x^2}\right \},\left \{y(x)\to a c_1+\sqrt {c_1{}^2-x^2}\right \}\right \}$ Maple : cpu = 0.237 (sec), leaf count = 161

$\left \{ y \left ( x \right ) =\sqrt {{a}^{2}-1}x,y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!{\frac {1}{ \left ( {{\it \_a}}^{2}+1 \right ) \left ( {{\it \_a}}^{2}-{a}^{2}+1 \right ) } \left ( -{{\it \_a}}^{3}+{\it \_a}\,{a}^{2}+\sqrt {{{\it \_a}}^{2}{a}^{2}-{a}^{4}+{a}^{2}}-{\it \_a} \right ) }{d{\it \_a}}+{\it \_C1} \right ) x,y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) -\int ^{{\it \_Z}}\!{\frac {1}{ \left ( {{\it \_a}}^{2}+1 \right ) \left ( {{\it \_a}}^{2}-{a}^{2}+1 \right ) } \left ( {{\it \_a}}^{3}-{\it \_a}\,{a}^{2}+\sqrt {{{\it \_a}}^{2}{a}^{2}-{a}^{4}+{a}^{2}}+{\it \_a} \right ) }{d{\it \_a}}+{\it \_C1} \right ) x,y \left ( x \right ) =-\sqrt {{a}^{2}-1}x \right \}$