2.498   ODE No. 498

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

\[ (3 y(x)-2) y'(x)^2+4 y(x)-4=0 \] Mathematica : cpu = 0.080699 (sec), leaf count = 107

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\sqrt {1-\text {$\#$1}} \sqrt {3 \text {$\#$1}-2}-\frac {\sin ^{-1}\left (\sqrt {3-3 \text {$\#$1}}\right )}{\sqrt {3}}\& \right ][-2 x+c_1]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\sqrt {1-\text {$\#$1}} \sqrt {3 \text {$\#$1}-2}-\frac {\sin ^{-1}\left (\sqrt {3-3 \text {$\#$1}}\right )}{\sqrt {3}}\& \right ][2 x+c_1]\right \}\right \}\] Maple : cpu = 0.763 (sec), leaf count = 99

\[ \left \{ y \left ( x \right ) =1,y \left ( x \right ) ={\frac {\sin \left ( {\it RootOf} \left ( -8\,\sqrt {3}{\it \_C1}\,{\it \_Z}+8\,\sqrt {3}x{\it \_Z}- \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}+48\,{{\it \_C1}}^{2}-96\,{\it \_C1}\,x+48\,{x}^{2}+{{\it \_Z}}^{2} \right ) \right ) }{6}}+{\frac {5}{6}},y \left ( x \right ) ={\frac {\sin \left ( {\it RootOf} \left ( 8\,\sqrt {3}{\it \_C1}\,{\it \_Z}-8\,\sqrt {3}x{\it \_Z}- \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}+48\,{{\it \_C1}}^{2}-96\,{\it \_C1}\,x+48\,{x}^{2}+{{\it \_Z}}^{2} \right ) \right ) }{6}}+{\frac {5}{6}} \right \} \]