Internal problem ID [3183]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y \left (y+x \right )+\left (x +2 y-1\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 93
dsolve(y(x)*(x+y(x))+(x+2*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {\left ({\mathrm e}^{x} x -{\mathrm e}^{x}-\sqrt {x^{2} {\mathrm e}^{2 x}-2 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x}-4 c_{1} {\mathrm e}^{x}}\right ) {\mathrm e}^{-x}}{2} y \left (x \right ) = -\frac {\left ({\mathrm e}^{x} x -{\mathrm e}^{x}+\sqrt {x^{2} {\mathrm e}^{2 x}-2 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x}-4 c_{1} {\mathrm e}^{x}}\right ) {\mathrm e}^{-x}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 11.91 (sec). Leaf size: 80
DSolve[y[x]*(x+y[x])+(x+2*y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-x-\frac {\sqrt {e^x (x-1)^2+4 c_1}}{\sqrt {e^x}}+1\right ) y(x)\to \frac {1}{2} \left (-x+\frac {\sqrt {e^x (x-1)^2+4 c_1}}{\sqrt {e^x}}+1\right ) \end{align*}