2.475   ODE No. 475

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

\[ 4 y(x) y'(x)^2+2 x y'(x)-y(x)=0 \] Mathematica : cpu = 0.0705002 (sec), leaf count = 57

\[\left \{\left \{y(x)\to -\frac {1}{2} e^{2 c_1} \sqrt {e^{4 c_1}-2 x}\right \},\left \{y(x)\to \frac {1}{2} e^{2 c_1} \sqrt {e^{4 c_1}-2 x}\right \}\right \}\]

Maple : cpu = 0.447 (sec), leaf count = 67

\[ \left \{ y \left ( x \right ) =\sqrt {{{\it \_C1}}^{2}-x{\it \_C1}},y \left ( x \right ) =\sqrt {{{\it \_C1}}^{2}+x{\it \_C1}},y \left ( x \right ) =-{\frac {i}{2}}x,y \left ( x \right ) ={\frac {i}{2}}x,y \left ( x \right ) =-\sqrt {{\it \_C1}\, \left ( x+{\it \_C1} \right ) },y \left ( x \right ) =-\sqrt {{{\it \_C1}}^{2}-x{\it \_C1}} \right \} \]