1.18 problem 18

Internal problem ID [1887]

Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 18.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y-y x -y^{\prime } x^{2}=0} \end {gather*}

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)
 

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

Solution by Mathematica

Time used: 0.03 (sec). Leaf size: 23

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

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