2.849   ODE No. 849

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

\[ y'(x)=x^2 \sqrt {x^2+4 y(x)-4 x}+\sqrt {x^2+4 y(x)-4 x}+x^3 \sqrt {x^2+4 y(x)-4 x}-\frac {x}{2}+1 \] Mathematica : cpu = 0.31874 (sec), leaf count = 73

\[\left \{\left \{y(x)\to -\frac {1}{6} \left (3 c_1-4\right ) x^4-\frac {2 c_1 x^3}{3}-2 c_1 x+c_1^2+\frac {x^8}{16}+\frac {x^7}{6}+\frac {x^6}{9}+\frac {x^5}{2}+\frac {3 x^2}{4}+x\right \}\right \}\]

Maple : cpu = 0.302 (sec), leaf count = 33

\[ \left \{ {\it \_C1}+{\frac {{x}^{4}}{2}}+{\frac {2\,{x}^{3}}{3}}+2\,x-\sqrt {{x}^{2}-4\,x+4\,y \left ( x \right ) }=0 \right \} \]