2.498   ODE No. 498

\[ (3 y(x)-2) y'(x)^2+4 y(x)-4=0 \]

✓ Mathematica : cpu = 0.107719 (sec), leaf count = 127

DSolve[-4 + 4*y[x] + (-2 + 3*y[x])*Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {\tan ^{-1}\left (\frac {\sqrt {3 \text {$\#$1}-2}}{\sqrt {3-3 \text {$\#$1}}}\right )}{\sqrt {3}}-\sqrt {1-\text {$\#$1}} \sqrt {3 \text {$\#$1}-2}\& \right ][-2 x+c_1]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\tan ^{-1}\left (\frac {\sqrt {3 \text {$\#$1}-2}}{\sqrt {3-3 \text {$\#$1}}}\right )}{\sqrt {3}}-\sqrt {1-\text {$\#$1}} \sqrt {3 \text {$\#$1}-2}\& \right ][2 x+c_1]\right \}\right \}\]

✓ Maple : cpu = 0.346 (sec), leaf count = 99

dsolve((3*y(x)-2)*diff(y(x),x)^2-4+4*y(x) = 0,y(x))
 

\[y \left (x \right ) = 1\]