63.1.46 problem 65

Internal problem ID [15486]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 65
Date solved : Thursday, October 02, 2025 at 10:18:28 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to x^2 \left (1+c_1 e^{\frac {1}{x}-2}\right ) \end{align*}

✓ Sympy. Time used: 0.181 (sec). Leaf size: 14

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

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