55.1.8 problem HW 1 problem 14

Internal problem ID [8704]
Book : Selected problems from homeworks from different courses
Section : Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale college, Bloomington, Minnesota
Problem number : HW 1 problem 14
Date solved : Sunday, March 30, 2025 at 01:24:10 PM
CAS classification : [_linear]

\begin{align*} x y-1+x^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=x*y(x)-1+x^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 14

ode=(x*y[x]-1)+x^2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\log (x)+c_1}{x} \]

✓ Sympy. Time used: 0.296 (sec). Leaf size: 8

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

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