87.1.9 problem 9

Internal problem ID [23221]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 9
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:24:33 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ y = c_1 \left (x \,{\mathrm e}^{\frac {1}{x}}+\operatorname {Ei}_{1}\left (-\frac {1}{x}\right )\right )+2 x +c_2 \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to -c_1 \operatorname {ExpIntegralEi}\left (\frac {1}{x}\right )+x \left (2+c_1 e^{\frac {1}{x}}\right )+c_2 \end{align*}

✓ Sympy. Time used: 0.599 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = C_{1} + C_{2} \left (x e^{\frac {1}{x}} - \operatorname {Ei}{\left (\frac {1}{x} \right )}\right ) + 2 x \]