Internal problem ID [8469]
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]
\[ \boxed {y^{\prime } x^{2}+y=x} \]
✓ 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)
\[ y \left (x \right ) = \left (\operatorname {Ei}_{1}\left (\frac {1}{x}\right )+c_{1} \right ) {\mathrm e}^{\frac {1}{x}} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 22
DSolve[x^2*y'[x] + y[x] - x==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{\frac {1}{x}} \left (-\operatorname {ExpIntegralEi}\left (-\frac {1}{x}\right )+c_1\right ) \]