12.2.26 problem 26

Internal problem ID [1562]
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 : 26
Date solved : Monday, January 27, 2025 at 05:00:12 AM
CAS classification : [_linear]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=\frac {2}{x^{2}+1} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve([(1+x^2)*diff(y(x),x)+4*x*y(x)=2/(1+x^2),y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 18

DSolve[{(1+x^2)*D[y[x],x]+4*x*y[x]==2/(1+x^2),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

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