Internal problem ID [3372]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 632.
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 (x -6 y\right )^{2} y^{\prime }+a +2 y x -6 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 115
dsolve((x-6*y(x))^2*diff(y(x),x)+a+2*x*y(x)-6*y(x)^2 = 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: 0.667 (sec). Leaf size: 115
DSolve[(x-6 y[x])^2 y'[x]+a+2 x y[x]-6 y[x]^2==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*}