69.12.13 problem 287

Internal problem ID [18166]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 287
Date solved : Thursday, October 02, 2025 at 03:06:28 PM
CAS classification : [_linear]

\begin{align*} \left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=(2*x-1)*diff(y(x),x)-2*y(x) = (1-4*x)/x^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 18

ode=(2*x-1)*D[y[x],x]-2*y[x]==(1-4*x)/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.313 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x - 1)*Derivative(y(x), x) - 2*y(x) - (1 - 4*x)/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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