18.1.16 problem Problem 14.23 (a)

Internal problem ID [3472]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.23 (a)
Date solved : Monday, January 27, 2025 at 07:38:14 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

\[ y \left (x \right ) = \frac {a^{2}}{3}+\frac {x^{2}}{3}+\frac {c_{1}}{\sqrt {a^{2}+x^{2}}} \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 31

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

\[ y(x)\to \frac {1}{3} \left (a^2+x^2\right )+\frac {c_1}{\sqrt {a^2+x^2}} \]