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 : Monday, January 27, 2025 at 05:00:22 AM
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*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

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

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

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