82.12.12 problem Ex. 12

Internal problem ID [18777]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 12
Date solved : Tuesday, January 28, 2025 at 12:16:52 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {4 x y}{x^{2}+1}&=\frac {1}{\left (x^{2}+1\right )^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(diff(y(x),x)+4*x/(x^2+1)*y(x)=1/(x^2+1)^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 18

DSolve[D[y[x],x]+4*x/(x^2+1)*y[x]==1/(x^2+1)^3,y[x],x,IncludeSingularSolutions -> True]
 

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