Internal problem ID [903]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+\frac {4 y}{x -1}=\frac {1}{\left (x -1\right )^{5}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{4}}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {-\cos \left (x \right )+\ln \left (x -1\right )+c_{1}}{\left (x -1\right )^{4}} \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 22
DSolve[y'[x] +4/(x-1)*y[x]==1/(x-1)^5+Sin[x]/(x-1)^4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\log (x-1)-\cos (x)+c_1}{(x-1)^4} \]