2.289   ODE No. 289

\[ a+(6 y(x)-x)^2 y'(x)-6 y(x)^2+2 x y(x)=0 \]

✓ Mathematica : cpu = 0.140756 (sec), leaf count = 115

DSolve[a + 2*x*y[x] - 6*y[x]^2 + (-x + 6*y[x])^2*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {1}{6} \left (x+\sqrt [3]{-18 a x-x^3+18 c_1}\right )\right \},\left \{y(x)\to \frac {x}{6}-\frac {1}{12} \left (1-i \sqrt {3}\right ) \sqrt [3]{-18 a x-x^3+18 c_1}\right \},\left \{y(x)\to \frac {x}{6}-\frac {1}{12} \left (1+i \sqrt {3}\right ) \sqrt [3]{-18 a x-x^3+18 c_1}\right \}\right \}\]

✓ Maple : cpu = 0.055 (sec), leaf count = 115

dsolve((6*y(x)-x)^2*diff(y(x),x)-6*y(x)^2+2*x*y(x)+a = 0,y(x))
 

\[y \left (x \right ) = \frac {\left (-x^{3}-18 a x -18 c_{1} \right )^{{1}/{3}}}{6}+\frac {x}{6}\]