12.2.15 problem 15

Internal problem ID [1551]
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
Date solved : Monday, January 27, 2025 at 04:59:44 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {{\mathrm e}^{-x^{2}}}{x^{2}+1} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

dsolve(diff(y(x),x) +(2*x)/(1+x^2)*y(x)=exp(-x^2)/(1+x^2),y(x), singsol=all)
 

\[ y = \frac {\sqrt {\pi }\, \operatorname {erf}\left (x \right )+2 c_1}{2 x^{2}+2} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 28

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

\[ y(x)\to \frac {\sqrt {\pi } \text {erf}(x)+2 c_1}{2 x^2+2} \]