29.17.9 problem 468

Internal problem ID [5066]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 468
Date solved : Monday, January 27, 2025 at 10:07:27 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 \left (x +y\right ) y^{\prime }+x^{2}+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 51

dsolve(2*(x+y(x))*diff(y(x),x)+x^2+2*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -x -\frac {\sqrt {-3 x^{3}+9 x^{2}-9 c_{1}}}{3} \\ y \left (x \right ) &= -x +\frac {\sqrt {-3 x^{3}+9 x^{2}-9 c_{1}}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.152 (sec). Leaf size: 53

DSolve[2(x+y[x])D[y[x],x]+x^2+2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x-\sqrt {-\frac {x^3}{3}+x^2+c_1} \\ y(x)\to -x+\sqrt {-\frac {x^3}{3}+x^2+c_1} \\ \end{align*}