Internal problem ID [913]
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: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x +3 y-\frac {2}{x \left (x^{2}+1\right )}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve([x*diff(y(x),x)+3*y(x)=2/(x*(1+x^2)),y(-1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (x^{2}+1\right )-\ln \relax (2)}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 19
DSolve[{x*y'[x]+3*y[x]==2/(x*(1+x^2)),y[-1]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log \left (\frac {1}{2} \left (x^2+1\right )\right )}{x^3} \\ \end{align*}