Internal problem ID [3860]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 610.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
\[ \boxed {\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (y+1\right )+\left (y+x \right )^{2} y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 110
dsolve((x+2*y(x)+y(x)^2)*diff(y(x),x)+y(x)*(1+y(x))+(x+y(x))^2*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{2}-c_{1} x +\sqrt {x^{4}-2 c_{1} x^{3}+\left (c_{1}^{2}-2\right ) x^{2}+\left (4+2 c_{1} \right ) x -4 c_{1} +1}-1}{-2 x +2 c_{1}} \\ y \left (x \right ) &= \frac {-x^{2}+c_{1} x +\sqrt {x^{4}-2 c_{1} x^{3}+\left (c_{1}^{2}-2\right ) x^{2}+\left (4+2 c_{1} \right ) x -4 c_{1} +1}+1}{2 x -2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.323 (sec). Leaf size: 146
DSolve[(x+2 y[x]+y[x]^2)y'[x]+y[x](1+y[x])+(x+y[x])^2 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2+\sqrt {\left (-x^2+c_1 x+1\right ){}^2+4 (x-c_1)}-c_1 x-1}{2 (x-c_1)} \\ y(x)\to \frac {-x^2+\sqrt {\left (-x^2+c_1 x+1\right ){}^2+4 (x-c_1)}+c_1 x+1}{2 (x-c_1)} \\ y(x)\to \frac {1}{2} \left (-\sqrt {x^2}-x\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {x^2}-x\right ) \\ \end{align*}