12.2.34 problem 34

Internal problem ID [1570]
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
Date solved : Monday, January 27, 2025 at 05:00:33 AM
CAS classification : [_linear]

\begin{align*} \left (x -1\right ) y^{\prime }+3 y&=\frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 21

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)
 

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

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 21

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

\[ y(x)\to \frac {\log (1-x)+\tan (x)+1}{(x-1)^3} \]