Internal problem ID [1084]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page
91
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {3 y x +2 y^{2}+y+\left (x^{2}+2 y x +x +2 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 85
dsolve((3*x*y(x)+2*y(x)^2+y(x))+(x^2+2*x*y(x)+x+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {-\sqrt {4+x^{2} \left (x +1\right )^{2} c_{1}^{2}}+\left (-x^{2}-x \right ) c_{1}}{2 c_{1} \left (x +1\right )} \\ y \left (x \right ) &= \frac {\sqrt {4+x^{2} \left (x +1\right )^{2} c_{1}^{2}}+\left (-x^{2}-x \right ) c_{1}}{2 c_{1} \left (x +1\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 14.424 (sec). Leaf size: 105
DSolve[(3*x*y[x]+2*y[x]^2+y[x])+(x^2+2*x*y[x]+x+2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-x-\sqrt {x^2+\frac {4 e^{c_1}}{(x+1)^2}}\right ) \\ y(x)\to \frac {1}{2} \left (-x+\sqrt {x^2+\frac {4 e^{c_1}}{(x+1)^2}}\right ) \\ 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*}