Internal problem ID [1992]
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) .
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {x y}{a^{2}+x^{2}}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x)+ (x*y(x))/(a^2+x^2)=x,y(x), singsol=all)
\[ y \relax (x ) = \frac {a^{2}}{3}+\frac {x^{2}}{3}+\frac {c_{1}}{\sqrt {a^{2}+x^{2}}} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 31
DSolve[y'[x]+ (x*y[x])/(a^2+x^2)==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (a^2+x^2\right )+\frac {c_1}{\sqrt {a^2+x^2}} \\ \end{align*}