75.5.4 problem 103

Internal problem ID [16669]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 103
Date solved : Monday, March 31, 2025 at 03:04:33 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 25

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

\begin{align*} y(x)\to \frac {x (\log (x)-1+c_1)}{\log (x)+c_1} \\ y(x)\to x \\ \end{align*}

✓ Sympy. Time used: 0.222 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = x \left (1 - 8 x^{2}\right ) \]