ODE No. 444

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

\[ x^2 y'(x)^2-(y(x)-2 x) y(x) y'(x)+y(x)^2=0 \] Mathematica : cpu = 0.157985 (sec), leaf count = 75

\[\left \{\left \{y(x)\to -\frac {\cosh \left (2 c_1\right )-\sinh \left (2 c_1\right )}{x \sinh \left (2 c_1\right )+x \cosh \left (2 c_1\right )-1}\right \},\left \{y(x)\to -\frac {\cosh \left (2 c_1\right )-\sinh \left (2 c_1\right )}{x \sinh \left (2 c_1\right )+x \cosh \left (2 c_1\right )+1}\right \}\right \}\] Maple : cpu = 25.128 (sec), leaf count = 120

\[ \left \{ y \left ( x \right ) ={\frac {{{\it \_C1}}^{3}\sqrt {2}-2\,{{\it \_C1}}^{2}x}{-2\,{{\it \_C1}}^{2}+4\,{x}^{2}}},y \left ( x \right ) ={\frac {{{\it \_C1}}^{2} \left ( {\it \_C1}\,\sqrt {2}+2\,x \right ) }{2\,{{\it \_C1}}^{2}-4\,{x}^{2}}},y \left ( x \right ) =4\,x,y \left ( x \right ) =-2\,{\frac {{{\it \_C1}}^{2} \left ( -{\it \_C1}\,\sqrt {2}+x \right ) }{-2\,{{\it \_C1}}^{2}+{x}^{2}}},y \left ( x \right ) =-2\,{\frac {{{\it \_C1}}^{2} \left ( {\it \_C1}\,\sqrt {2}+x \right ) }{-2\,{{\it \_C1}}^{2}+{x}^{2}}} \right \} \]