Internal problem ID [901]
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: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+\frac {2 x y}{x^{2}+1}-\frac {{\mathrm e}^{-x^{2}}}{x^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x) +(2*x)/(1+x^2)*y(x)=exp(-x^2)/(1+x^2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\frac {\sqrt {\pi }\, \operatorname {erf}\left (x \right )}{2}+c_{1}}{x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 28
DSolve[y'[x] +(2*x)/(1+x^2)*y[x]==Exp[-x^2]/(1+x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {\pi } \text {erf}(x)+2 c_1}{2 x^2+2} \\ \end{align*}