54.1.174 problem 177

Internal problem ID [11488]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 177
Date solved : Tuesday, September 30, 2025 at 08:39:18 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {x^{2}}{1+c_1 \left (x -1\right )} \]

✓ Mathematica. Time used: 0.195 (sec). Leaf size: 85

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

\begin{align*} y(x)&\to \frac {\exp \left (\int _1^x\frac {K[1]-2}{(K[1]-1) K[1]}dK[1]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {K[1]-2}{(K[1]-1) K[1]}dK[1]\right )}{(K[2]-1) K[2]^2}dK[2]+c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.185 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {x^{2}}{C_{1} x - C_{1} + 1} \]