Internal problem ID [12364]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{\prime }+\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 69
dsolve(diff(y(x),x)=-y(x)*(2*x+y(x))/(x*(2*y(x)+x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {x^{2} c_{1}^{2}-\sqrt {c_{1}^{4} x^{4}+4 c_{1} x}}{2 x \,c_{1}^{2}} y \left (x \right ) = -\frac {x^{2} c_{1}^{2}+\sqrt {c_{1}^{4} x^{4}+4 c_{1} x}}{2 x \,c_{1}^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 1.084 (sec). Leaf size: 118
DSolve[y'[x]==-y[x]*(2*x+y[x])/(x*(2*y[x]+x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-x-\frac {\sqrt {x^3+4 e^{c_1}}}{\sqrt {x}}\right ) y(x)\to \frac {1}{2} \left (-x+\frac {\sqrt {x^3+4 e^{c_1}}}{\sqrt {x}}\right ) y(x)\to -\frac {x^{3/2}+\sqrt {x^3}}{2 \sqrt {x}} y(x)\to \frac {\sqrt {x^3}}{2 \sqrt {x}}-\frac {x}{2} \end{align*}