Internal problem ID [3562]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 306.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (a^{2}+x^{2}\right ) y^{\prime }-\left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve((a^2+x^2)*diff(y(x),x) = (b+y(x))*(x+sqrt(a^2+x^2)),y(x), singsol=all)
\[ y \left (x \right ) = \left (\frac {x b}{\sqrt {a^{2}+x^{2}}\, a^{2}}+c_{1} \right ) \left (x \sqrt {a^{2}+x^{2}}+a^{2}+x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.28 (sec). Leaf size: 81
DSolve[(a^2+x^2)y'[x]==(b+y[x])(x+Sqrt[a^2+x^2]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (x \left (x-\sqrt {a^2+x^2}\right )+a^2\right ) \left (b x-c_1 \sqrt {a^2+x^2}\right )}{\sqrt {a^2+x^2} \left (x-\sqrt {a^2+x^2}\right )^2} y(x)\to -b \end{align*}