12.2.30 problem 30

Internal problem ID [1566]
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 : 30
Date solved : Saturday, March 29, 2025 at 10:59:24 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.038 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 25

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

\[ y(x)\to \frac {\log (x-1)-\cos (x)-i \pi }{(x-1)^3} \]

✓ Sympy. Time used: 0.940 (sec). Leaf size: 27

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

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