Internal problem ID [7869]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 289.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]]]
Solve \begin {gather*} \boxed {\left (6 y-x \right )^{2} y^{\prime }-6 y^{2}+2 y x +a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 115
dsolve((6*y(x)-x)^2*diff(y(x),x)-6*y(x)^2+2*x*y(x)+a=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (-x^{3}-18 a x -18 c_{1}\right )^{\frac {1}{3}}}{6}+\frac {x}{6} \\ y \relax (x ) = -\frac {\left (-x^{3}-18 a x -18 c_{1}\right )^{\frac {1}{3}}}{12}-\frac {i \sqrt {3}\, \left (-x^{3}-18 a x -18 c_{1}\right )^{\frac {1}{3}}}{12}+\frac {x}{6} \\ y \relax (x ) = -\frac {\left (-x^{3}-18 a x -18 c_{1}\right )^{\frac {1}{3}}}{12}+\frac {i \sqrt {3}\, \left (-x^{3}-18 a x -18 c_{1}\right )^{\frac {1}{3}}}{12}+\frac {x}{6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.052 (sec). Leaf size: 115
DSolve[(6*y[x]-x)^2*y'[x]-6*y[x]^2+2*x*y[x]+a==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (x+\sqrt [3]{-18 a x-x^3+18 c_1}\right ) \\ y(x)\to \frac {x}{6}+\frac {1}{12} i \left (\sqrt {3}+i\right ) \sqrt [3]{-18 a x-x^3+18 c_1} \\ 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} \\ \end{align*}