12.2.27 problem 27

Internal problem ID [1563]
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
Date solved : Monday, January 27, 2025 at 05:00:15 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.014 (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)
 

\[ y = \frac {\ln \left (x^{2}+1\right )-\ln \left (2\right )}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 19

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

\[ y(x)\to \frac {\log \left (\frac {1}{2} \left (x^2+1\right )\right )}{x^3} \]