2.434   ODE No. 434

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

✓ Mathematica : cpu = 0.0676489 (sec), leaf count = 123

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

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

✓ Maple : cpu = 0.007 (sec), leaf count = 7

dsolve(diff(y(x),x)-1 = 0,y(x))
 

\[y \left (x \right ) = x +c_{1}\]