2.270   ODE No. 270

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

\[ x^2+\left (y(x)^2-x\right ) y'(x)-y(x)=0 \] Mathematica : cpu = 11.1423 (sec), leaf count = 326

\[\left \{\left \{y(x)\to -\frac {\sqrt [3]{2} \left (\sqrt {\left (6 c_1-4\right ) x^3+9 c_1^2+x^6}+3 c_1+x^3\right ){}^{2/3}+2 x}{2^{2/3} \sqrt [3]{\sqrt {\left (6 c_1-4\right ) x^3+9 c_1^2+x^6}+3 c_1+x^3}}\right \},\left \{y(x)\to \frac {\sqrt [3]{2} \left (1-i \sqrt {3}\right ) \left (\sqrt {\left (6 c_1-4\right ) x^3+9 c_1^2+x^6}+3 c_1+x^3\right ){}^{2/3}+\left (2+2 i \sqrt {3}\right ) x}{2\ 2^{2/3} \sqrt [3]{\sqrt {\left (6 c_1-4\right ) x^3+9 c_1^2+x^6}+3 c_1+x^3}}\right \},\left \{y(x)\to \frac {\sqrt [3]{2} \left (1+i \sqrt {3}\right ) \left (\sqrt {\left (6 c_1-4\right ) x^3+9 c_1^2+x^6}+3 c_1+x^3\right ){}^{2/3}+\left (2-2 i \sqrt {3}\right ) x}{2\ 2^{2/3} \sqrt [3]{\sqrt {\left (6 c_1-4\right ) x^3+9 c_1^2+x^6}+3 c_1+x^3}}\right \}\right \}\]

Maple : cpu = 0.025 (sec), leaf count = 319

\[ \left \{ y \left ( x \right ) ={\frac {1}{2} \left ( \left ( -4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,x \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}}}}}},y \left ( x \right ) =-{\frac {1}{4} \left ( \left ( i \left ( -4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,ix \right ) \sqrt {3}+ \left ( -4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,x \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}}}}}},y \left ( x \right ) ={\frac {1}{4} \left ( i\sqrt {3} \left ( -4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,i\sqrt {3}x- \left ( -4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,x \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}}}}}} \right \} \]