6.2.34 problem 34

Internal problem ID [1570]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 34
Date solved : Tuesday, September 30, 2025 at 04:36:44 AM
CAS classification : [_linear]

\begin{align*} \left (x -1\right ) y^{\prime }+3 y&=\frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.050 (sec). Leaf size: 21

ode:=(x-1)*diff(y(x),x)+3*y(x) = (1+(x-1)*sec(x)^2)/(x-1)^3; 
ic:=[y(0) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\ln \left (x -1\right )+\tan \left (x \right )+1-i \pi }{\left (x -1\right )^{3}} \]

✓ Mathematica. Time used: 0.102 (sec). Leaf size: 21

ode=(x-1)*D[y[x],x]+3*y[x]==(1+(x-1)*Sec[x]^2)/(x-1)^3; 
ic=y[0]==-1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\log (1-x)+\tan (x)+1}{(x-1)^3} \end{align*}

✓ Sympy. Time used: 0.594 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 1)*Derivative(y(x), x) + 3*y(x) - ((x - 1)/cos(x)**2 + 1)/(x - 1)**3,0) 
ics = {y(0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\log {\left (x - 1 \right )} + \tan {\left (x \right )} + 1 - i \pi }{x^{3} - 3 x^{2} + 3 x - 1} \]