50.8.2 problem 1(b)

Internal problem ID [7918]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 1(b)
Date solved : Sunday, March 30, 2025 at 12:37:16 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 1.164 (sec). Leaf size: 24

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

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