32.2.43 problem 44

Internal problem ID [7760]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 44
Date solved : Tuesday, September 30, 2025 at 05:04:59 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ y = \frac {-x^{2}+2 c_1}{2 x^{3}-2 x} \]

✓ Mathematica. Time used: 0.201 (sec). Leaf size: 90

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

\begin{align*} y(x)&\to \exp \left (\int _1^x-\frac {1-3 K[1]^2}{K[1]-K[1]^3}dK[1]\right ) \left (\int _1^x\frac {\exp \left (-\int _1^{K[2]}-\frac {1-3 K[1]^2}{K[1]-K[1]^3}dK[1]\right )}{1-K[2]^2}dK[2]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.194 (sec). Leaf size: 14

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

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