63.1.39 problem 58

Internal problem ID [15479]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 58
Date solved : Thursday, October 02, 2025 at 10:18:17 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {a y}{x}&=\frac {1+x}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 31

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

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

✓ Mathematica. Time used: 1.076 (sec). Leaf size: 28

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

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

✓ Sympy. Time used: 0.170 (sec). Leaf size: 27

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

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