60.1.130 problem 133

Internal problem ID [10144]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 133
Date solved : Sunday, March 30, 2025 at 03:19:53 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=x^2*diff(y(x),x)+y(x)-x = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\operatorname {Ei}_{1}\left (\frac {1}{x}\right )+c_1 \right ) {\mathrm e}^{\frac {1}{x}} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 22

ode=x^2*D[y[x],x] + y[x] - x==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.968 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) - x + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} - \operatorname {Ei}{\left (- \frac {1}{x} \right )}\right ) e^{\frac {1}{x}} \]