28.1.106 problem 129

Internal problem ID [4412]
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 : 129
Date solved : Monday, January 27, 2025 at 09:15:11 AM
CAS classification : [_separable]

\begin{align*} y x +2 x^{3} y+x^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve((x*y(x)+2*x^3*y(x))+(x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{-x^{2}}}{x} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 23

DSolve[(x*y[x]+2*x^3*y[x])+(x^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1 e^{-x^2}}{x} \\ y(x)\to 0 \\ \end{align*}