60.1.251 problem 256

Internal problem ID [10265]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 256
Date solved : Sunday, March 30, 2025 at 03:35:22 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 29

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

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

✓ Mathematica. Time used: 0.146 (sec). Leaf size: 42

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]-1}{K[1]}dK[1]\&\right ]\left [-\frac {1}{x}-\log (x)+1+c_1\right ] \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.471 (sec). Leaf size: 14

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

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