Internal problem ID [916]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (x -1\right ) y^{\prime }+3 y=\frac {1}{\left (x -1\right )^{3}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{2}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
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)
\[ y \left (x \right ) = \frac {-\cos \left (x \right )+\ln \left (x -1\right )-i \pi }{\left (x -1\right )^{3}} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 25
DSolve[{(x-1)*y'[x]+3*y[x]==1/(x-1)^3+Sin[x]/(x-1)^2,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\log (x-1)-\cos (x)-i \pi }{(x-1)^3} \]