12.2.17 problem 17

Internal problem ID [1553]
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 : 17
Date solved : Monday, January 27, 2025 at 04:59:48 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {4 y}{x -1}&=\frac {1}{\left (x -1\right )^{5}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{4}} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 20

dsolve(diff(y(x),x) +4/(x-1)*y(x)=1/(x-1)^5+sin(x)/(x-1)^4,y(x), singsol=all)
 

\[ y = \frac {-\cos \left (x \right )+\ln \left (x -1\right )+c_1}{\left (x -1\right )^{4}} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 22

DSolve[D[y[x],x] +4/(x-1)*y[x]==1/(x-1)^5+Sin[x]/(x-1)^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\log (x-1)-\cos (x)+c_1}{(x-1)^4} \]