60.1.132 problem 135

Internal problem ID [10146]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 135
Date solved : Wednesday, March 05, 2025 at 08:33:37 AM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime }-\left (x -1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

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

\[ y = c_{1} {\mathrm e}^{\frac {1}{x}} x \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 21

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

\begin{align*} y(x)\to c_1 e^{\frac {1}{x}-1} x \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.309 (sec). Leaf size: 10

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

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