#### 2.492   ODE No. 492

$\left (y(x)^2-a^2\right ) y'(x)^2+y(x)^2=0$ Mathematica : cpu = 0.0802164 (sec), leaf count = 97

$\left \{\left \{y(x)\to \text {InverseFunction}\left [\sqrt {a^2-\text {\#1}^2}-a \tanh ^{-1}\left (\frac {\sqrt {a^2-\text {\#1}^2}}{a}\right )\& \right ][c_1-x]\right \},\left \{y(x)\to \text {InverseFunction}\left [\sqrt {a^2-\text {\#1}^2}-a \tanh ^{-1}\left (\frac {\sqrt {a^2-\text {\#1}^2}}{a}\right )\& \right ][c_1+x]\right \}\right \}$ Maple : cpu = 1.684 (sec), leaf count = 122

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