Internal problem ID [920]
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: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x -1\right ) y^{\prime }+3 y-\frac {1+\left (x -1\right ) \left (\sec ^{2}\relax (x )\right )}{\left (x -1\right )^{3}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 22
dsolve([(x-1)*diff(y(x),x)+3*y(x)= (1+(x-1)*sec(x)^2)/(x-1)^3,y(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (x -1\right )+\tan \relax (x )+1-i \pi }{\left (x -1\right )^{3}} \]
✓ Solution by Mathematica
Time used: 0.178 (sec). Leaf size: 21
DSolve[{(x-1)*y'[x]+3*y[x]==(1+(x-1)*Sec[x]^2)/(x-1)^3,y[0]==-1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log (1-x)+\tan (x)+1}{(x-1)^3} \\ \end{align*}