#### 2.498   ODE No. 498

$(3 y(x)-2) y'(x)^2+4 y(x)-4=0$ Mathematica : cpu = 0.0775503 (sec), leaf count = 107

$\left \{\left \{y(x)\to \text {InverseFunction}\left [-\sqrt {1-\text {\#1}} \sqrt {3 \text {\#1}-2}-\frac {\sin ^{-1}\left (\sqrt {3-3 \text {\#1}}\right )}{\sqrt {3}}\& \right ][c_1-2 x]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\sqrt {1-\text {\#1}} \sqrt {3 \text {\#1}-2}-\frac {\sin ^{-1}\left (\sqrt {3-3 \text {\#1}}\right )}{\sqrt {3}}\& \right ][c_1+2 x]\right \}\right \}$ Maple : cpu = 1.002 (sec), leaf count = 99

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