Internal problem ID [905]
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: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {2 y+y^{\prime } x -\frac {2}{x^{2}}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x*diff(y(x),x) +2*y(x)=2/x^2+1,y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {x^{2}}{2}+2 \ln \relax (x )+c_{1}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 22
DSolve[x*y'[x] +2*y[x]==2/x^2+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 \log (x)}{x^2}+\frac {c_1}{x^2}+\frac {1}{2} \\ \end{align*}