28.1.117 problem 140

Internal problem ID [4423]
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 : 140
Date solved : Monday, January 27, 2025 at 09:16:47 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(x^2*(x*diff(y(x),x)-y(x) )=(x+y(x))*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x}{-1+c_{1} {\mathrm e}^{\frac {1}{x}}} \]

✓ Solution by Mathematica

Time used: 0.178 (sec). Leaf size: 24

DSolve[x^2*(x*D[y[x],x]-y[x] )==(x+y[x])*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x}{-1+c_1 e^{\frac {1}{x}}} \\ y(x)\to 0 \\ \end{align*}