60.1.133 problem 134

Internal problem ID [10147]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 134
Date solved : Monday, January 27, 2025 at 06:29:59 PM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x) - y(x) + x^2*exp(x-1/x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 21

DSolve[x^2*D[y[x],x] - y[x] + x^2*Exp[x-1/x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-1/x} \left (-e^x+c_1\right ) \]