19.2.4 problem 4

Internal problem ID [3533]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.6, page 50
Problem number : 4
Date solved : Monday, January 27, 2025 at 07:40:53 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 24

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

\[ y(x)\to \frac {x^4+2 x^2+c_1}{x^2+1} \]