11.14 problem 305

Internal problem ID [3053]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 11
Problem number: 305.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {\left (a^{2}+x^{2}\right ) y^{\prime }-b -y x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 22

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

\[ y \relax (x ) = \frac {x b}{a^{2}}+\sqrt {a^{2}+x^{2}}\, c_{1} \]

Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 26

DSolve[(a^2+x^2)y'[x]==b+x y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {b x}{a^2}+c_1 \sqrt {a^2+x^2} \\ \end{align*}