Internal problem ID [2674]
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]]
Solve \begin {gather*} \boxed {y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime }=0} \end {gather*}
✓ 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 \relax (x ) = -\frac {\left (x \,{\mathrm e}^{x}-{\mathrm e}^{x}-\sqrt {{\mathrm e}^{2 x} x^{2}-2 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x}-4 c_{1} {\mathrm e}^{x}}\right ) {\mathrm e}^{-x}}{2} \\ y \relax (x ) = -\frac {\left (x \,{\mathrm e}^{x}-{\mathrm e}^{x}+\sqrt {{\mathrm e}^{2 x} x^{2}-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: 11.921 (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*}