85.33.10 problem 10

Internal problem ID [22633]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 10
Date solved : Thursday, October 02, 2025 at 08:57:04 PM
CAS classification : [_linear]

\begin{align*} y x +x^{2} y^{\prime }&=1+x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=x^2*diff(y(x),x)+x*y(x) = 1+x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x +\ln \left (x \right )+c_1}{x} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 15

ode=x^2*D[y[x],x]+x*y[x]==x+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x+\log (x)+c_1}{x} \end{align*}

✓ Sympy. Time used: 0.215 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) + x*y(x) - x - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + x + \log {\left (x \right )}}{x} \]