Internal problem ID [3267]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 523.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (4+y\right ) y^{\prime }-2 x -2 y-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 145
dsolve(x*(4+y(x))*diff(y(x),x) = 2*x+2*y(x)+y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (x +4\right )^{\frac {3}{2}} \sqrt {\frac {c_{1} x +4 c_{1}-4}{x +4}}\, x +4 x^{\frac {3}{2}}+16 \sqrt {x}}{\left (x +4\right )^{\frac {3}{2}} \sqrt {\frac {c_{1} x +4 c_{1}-4}{x +4}}-x^{\frac {3}{2}}-4 \sqrt {x}} \\ y \relax (x ) = \frac {\left (x +4\right )^{\frac {3}{2}} \sqrt {\frac {c_{1} x +4 c_{1}-4}{x +4}}\, x -4 x^{\frac {3}{2}}-16 \sqrt {x}}{\left (x +4\right )^{\frac {3}{2}} \sqrt {\frac {c_{1} x +4 c_{1}-4}{x +4}}+x^{\frac {3}{2}}+4 \sqrt {x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.993 (sec). Leaf size: 90
DSolve[x(4+y[x])y'[x]==2 x+2 y[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 x+\sqrt {x} \sqrt {x+4} \sqrt {-\frac {4}{x+4}+c_1}}{-1+c_1} \\ y(x)\to -4+\frac {1}{\frac {1}{x+4}+\frac {\sqrt {x}}{(x+4)^{3/2} \sqrt {-\frac {4}{x+4}+c_1}}} \\ y(x)\to x \\ \end{align*}