Internal problem ID [8470]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 134.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{2} y^{\prime }-y=-x^{2} {\mathrm e}^{x -\frac {1}{x}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x) - y(x) + x^2*exp(x-1/x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (-{\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-\frac {1}{x}} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 21
DSolve[x^2*y'[x] - y[x] + x^2*Exp[x-1/x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-1/x} \left (-e^x+c_1\right ) \]