2.281   ODE No. 281

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

\[ \left (-x^2+2 x y(x)+y(x)^2\right ) y'(x)+x^2+2 x y(x)-y(x)^2=0 \] Mathematica : cpu = 0.181596 (sec), leaf count = 75

\[\left \{\left \{y(x)\to \frac {1}{2} \left (e^{c_1}-\sqrt {-4 x^2+4 e^{c_1} x+e^{2 c_1}}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {-4 x^2+4 e^{c_1} x+e^{2 c_1}}+e^{c_1}\right )\right \}\right \}\] Maple : cpu = 0.049 (sec), leaf count = 55

\[ \left \{ y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}} \left ( 1+\sqrt {-4\,{{\it \_C1}}^{2}{x}^{2}+4\,{\it \_C1}\,x+1} \right ) },y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}} \left ( 1-\sqrt {-4\,{{\it \_C1}}^{2}{x}^{2}+4\,{\it \_C1}\,x+1} \right ) } \right \} \]