3.407   ODE No. 407

\[ \boxed { x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-y \left ( x \right ) =0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 0.020503 (sec), leaf count = 51 \[ \left \{\left \{y(x)\to \frac {1}{4} \left (-4 c_1 \sqrt {x}+c_1^2+4 x\right )\right \},\left \{y(x)\to \frac {1}{4} \left (4 c_1 \sqrt {x}+c_1^2+4 x\right )\right \}\right \} \]

Maple: cpu = 0.499 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) ={\frac {1}{x} \left ( -x+\sqrt {{\it \_C1}\,x} \right ) ^{2}},y \left ( x \right ) ={ \frac {1}{x} \left ( x+\sqrt {{\it \_C1}\,x} \right ) ^{2}} \right \} \]