3.498   ODE No. 498

\[ \boxed { \left ( 3\,y \left ( x \right ) -2 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-4+4\,y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.103513 (sec), leaf count = 107 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [-\sqrt {1-\text {$\#$1}} \sqrt {3 \text {$\#$1}-2}-\frac {\sin ^{-1}\left (\sqrt {3-3 \text {$\#$1}}\right )}{\sqrt {3}}\& \right ]\left [c_1-2 x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\sqrt {1-\text {$\#$1}} \sqrt {3 \text {$\#$1}-2}-\frac {\sin ^{-1}\left (\sqrt {3-3 \text {$\#$1}}\right )}{\sqrt {3}}\& \right ]\left [c_1+2 x\right ]\right \}\right \} \]

Maple: cpu = 0.749 (sec), leaf count = 99 \[ \left \{ y \left ( x \right ) =1,y \left ( x \right ) ={\frac {\sin \left ( {\it RootOf} \left ( -8\,\sqrt {3}{\it \_C1}\,{\it \_Z}+8\, \sqrt {3}x{\it \_Z}- \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2 }+48\,{{\it \_C1}}^{2}-96\,{\it \_C1}\,x+48\,{x}^{2}+{{\it \_Z}}^{2} \right ) \right ) }{6}}+{\frac {5}{6}},y \left ( x \right ) ={\frac { \sin \left ( {\it RootOf} \left ( 8\,\sqrt {3}{\it \_C1}\,{\it \_Z}-8\, \sqrt {3}x{\it \_Z}- \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2 }+48\,{{\it \_C1}}^{2}-96\,{\it \_C1}\,x+48\,{x}^{2}+{{\it \_Z}}^{2} \right ) \right ) }{6}}+{\frac {5}{6}} \right \} \]