69.1.126 problem 185

Internal problem ID [14200]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 185
Date solved : Wednesday, March 05, 2025 at 10:39:43 PM
CAS classification : [_linear]

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

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

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

\[ y = c_{1} \sqrt {x^{2}+1}+\alpha x \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 21

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

\[ y(x)\to a x+c_1 \sqrt {x^2+1} \]

✓ Sympy. Time used: 1.742 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \mathrm {A} x + C_{1} \sqrt {x^{2} + 1} \]