28.1.38 problem 38

Internal problem ID [4344]
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
Date solved : Monday, January 27, 2025 at 09:06:17 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 63

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 {x}{2}+\frac {1}{2}+\frac {\sqrt {{\mathrm e}^{x} \left (\left (x -1\right )^{2} {\mathrm e}^{x}-4 c_{1} \right )}\, {\mathrm e}^{-x}}{2} \\ y \left (x \right ) &= -\frac {x}{2}+\frac {1}{2}-\frac {\sqrt {{\mathrm e}^{x} \left (\left (x -1\right )^{2} {\mathrm e}^{x}-4 c_{1} \right )}\, {\mathrm e}^{-x}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 11.798 (sec). Leaf size: 80

DSolve[y[x]*(x+y[x])+(x+2*y[x]-1)*D[y[x],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*}