Internal problem ID [7713]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 133.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x^2*diff(y(x),x) + y(x) - x=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\expIntegral \left (1, \frac {1}{x}\right )+c_{1}\right ) {\mathrm e}^{\frac {1}{x}} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 22
DSolve[x^2*y'[x] + y[x] - x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {1}{x}} \left (-\text {Ei}\left (-\frac {1}{x}\right )+c_1\right ) \\ \end{align*}