15.1.18 problem 18

Internal problem ID [2858]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 18
Date solved : Monday, January 27, 2025 at 06:20:20 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

\[ y = \frac {c_1 \,{\mathrm e}^{-\frac {1}{x}}}{x} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 23

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

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