2.448   ODE No. 448

\[ \left (x^2-1\right ) y'(x)^2-y(x)^2+1=0 \] Mathematica : cpu = 0.108614 (sec), leaf count = 349


\[\left \{\left \{y(x)\to -\frac {1}{2} e^{-c_1} \sqrt {2 x^2+2 e^{4 c_1} x^2-2 \sqrt {(x-1) (x+1)} x+2 e^{4 c_1} \sqrt {(x-1) (x+1)} x-1+2 e^{2 c_1}-e^{4 c_1}}\right \},\left \{y(x)\to \frac {1}{2} e^{-c_1} \sqrt {2 x^2+2 e^{4 c_1} x^2-2 \sqrt {(x-1) (x+1)} x+2 e^{4 c_1} \sqrt {(x-1) (x+1)} x-1+2 e^{2 c_1}-e^{4 c_1}}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {2 e^{-2 c_1} x^2+2 e^{2 c_1} x^2+2 e^{-2 c_1} \sqrt {x^2-1} x-2 e^{2 c_1} \sqrt {x^2-1} x+2-e^{-2 c_1}-e^{2 c_1}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {2 e^{-2 c_1} x^2+2 e^{2 c_1} x^2+2 e^{-2 c_1} \sqrt {x^2-1} x-2 e^{2 c_1} \sqrt {x^2-1} x+2-e^{-2 c_1}-e^{2 c_1}}\right \}\right \}\] Maple : cpu = 0. (sec), leaf count = 0


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