#### 2.546   ODE No. 546

$y'(x)^4+3 (x-1) y'(x)^2-3 (2 y(x)-1) y'(x)+3 x=0$ Mathematica : cpu = 0.0290142 (sec), leaf count = 113

$\left \{\left \{y(x)\to \frac {1}{12} \left (-\sqrt {48 c_1{}^2 x^2+12 c_1{}^4 x+c_1{}^6+64 x^3}-6 c_1 x-c_1{}^3+6 c_1+6\right )\right \},\left \{y(x)\to \frac {1}{12} \left (\sqrt {48 c_1{}^2 x^2+12 c_1{}^4 x+c_1{}^6+64 x^3}-6 c_1 x-c_1{}^3+6 c_1+6\right )\right \}\right \}$ Maple : cpu = 0.094 (sec), leaf count = 171

$\left \{ y \left ( x \right ) ={1 \left ( \left ( -6+{{\it \_C1}}^{3}+ \left ( 6\,x-6 \right ) {\it \_C1} \right ) \sqrt {{{\it \_C1}}^{2}+4\,x}-2\,{{\it \_C1}}^{4}+ \left ( -14\,x+6 \right ) {{\it \_C1}}^{2}+ \left ( \left ( {{\it \_C1}}^{2}+4\,x \right ) ^{{\frac {3}{2}}}+6 \right ) {\it \_C1}-16\,{x}^{2} \right ) \left ( -12\,\sqrt {{{\it \_C1}}^{2}+4\,x}+12\,{\it \_C1} \right ) ^{-1}},y \left ( x \right ) ={1 \left ( \left ( 6-{{\it \_C1}}^{3}+ \left ( -6\,x+6 \right ) {\it \_C1} \right ) \sqrt {{{\it \_C1}}^{2}+4\,x}-2\,{{\it \_C1}}^{4}+ \left ( -14\,x+6 \right ) {{\it \_C1}}^{2}+ \left ( - \left ( {{\it \_C1}}^{2}+4\,x \right ) ^{{\frac {3}{2}}}+6 \right ) {\it \_C1}-16\,{x}^{2} \right ) \left ( 12\,{\it \_C1}+12\,\sqrt {{{\it \_C1}}^{2}+4\,x} \right ) ^{-1}},y \left ( x \right ) =-x+{\frac {5}{6}},y \left ( x \right ) =x+{\frac {1}{6}} \right \}$