2.431   ODE No. 431

\[ x^2 y'(x)^2-y(x)^4+y(x)^2=0 \]

✓ Mathematica : cpu = 0.0582197 (sec), leaf count = 81

DSolve[y[x]^2 - y[x]^4 + x^2*Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\sqrt {1+\tan ^2(-\log (x)+c_1)}\right \},\left \{y(x)\to \sqrt {1+\tan ^2(-\log (x)+c_1)}\right \},\left \{y(x)\to -\sqrt {1+\tan ^2(\log (x)+c_1)}\right \},\left \{y(x)\to \sqrt {1+\tan ^2(\log (x)+c_1)}\right \}\right \}\]

✓ Maple : cpu = 0.185 (sec), leaf count = 62

dsolve(x^2*diff(y(x),x)^2-y(x)^4+y(x)^2 = 0,y(x))
 

\[y \left (x \right ) = -1\]