2.708   ODE No. 708

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

\[ y'(x)=\frac {\left (4 a x-y(x)^2\right )^3}{y(x) \left (4 a x-y(x)^2-1\right )} \] Mathematica : cpu = 0.275752 (sec), leaf count = 89

\[\text {Solve}\left [2 a \left (x-\frac {\text {RootSum}\left [-\text {$\#$1}^3+2 \text {$\#$1} a-2 a\& ,\frac {\text {$\#$1} a \log \left (-\text {$\#$1}+4 a x-y(x)^2\right )-a \log \left (-\text {$\#$1}+4 a x-y(x)^2\right )}{2 a-3 \text {$\#$1}^2}\& \right ]}{2 a}\right )=c_1,y(x)\right ]\]

Maple : cpu = 0.946 (sec), leaf count = 308

\[ \left \{ \int _{{\it \_b}}^{x}\!-{\frac { \left ( 4\,{\it \_a}\,a- \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{3}}{64\,{{\it \_a}}^{3}{a}^{3}-48\,{{\it \_a}}^{2}{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}+12\,{\it \_a}\,a \left ( y \left ( x \right ) \right ) ^{4}- \left ( y \left ( x \right ) \right ) ^{6}-8\,{\it \_a}\,{a}^{2}+2\,a \left ( y \left ( x \right ) \right ) ^{2}+2\,a}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!{\frac { \left ( -{{\it \_f}}^{2}+4\,ax-1 \right ) {\it \_f}}{-{{\it \_f}}^{6}+12\,{{\it \_f}}^{4}ax-48\,{{\it \_f}}^{2}{a}^{2}{x}^{2}+64\,{a}^{3}{x}^{3}+2\,{{\it \_f}}^{2}a-8\,{a}^{2}x+2\,a}}-\int _{{\it \_b}}^{x}\!{\frac { \left ( 4\,{\it \_a}\,a-{{\it \_f}}^{2} \right ) ^{3} \left ( -96\,{{\it \_a}}^{2}{\it \_f}\,{a}^{2}+48\,{\it \_a}\,{{\it \_f}}^{3}a-6\,{{\it \_f}}^{5}+4\,{\it \_f}\,a \right ) }{ \left ( 64\,{{\it \_a}}^{3}{a}^{3}-48\,{{\it \_a}}^{2}{{\it \_f}}^{2}{a}^{2}+12\,{\it \_a}\,{{\it \_f}}^{4}a-{{\it \_f}}^{6}-8\,{\it \_a}\,{a}^{2}+2\,{{\it \_f}}^{2}a+2\,a \right ) ^{2}}}+6\,{\frac { \left ( 4\,{\it \_a}\,a-{{\it \_f}}^{2} \right ) ^{2}{\it \_f}}{64\,{{\it \_a}}^{3}{a}^{3}-48\,{{\it \_a}}^{2}{{\it \_f}}^{2}{a}^{2}+12\,{\it \_a}\,{{\it \_f}}^{4}a-{{\it \_f}}^{6}-8\,{\it \_a}\,{a}^{2}+2\,{{\it \_f}}^{2}a+2\,a}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]