69.6.2 problem 126

Internal problem ID [18045]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 126
Date solved : Thursday, October 02, 2025 at 02:35:53 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 14

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

\[ y = \frac {x^{3}-1}{3 x} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to \frac {x^3-1}{3 x} \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {\frac {x^{3}}{3} - \frac {1}{3}}{x} \]