29.11.15 problem 306

Internal problem ID [4906]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 306
Date solved : Monday, January 27, 2025 at 09:47:28 AM
CAS classification : [_separable]

\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime }&=\left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 53

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

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

✓ Solution by Mathematica

Time used: 0.284 (sec). Leaf size: 81

DSolve[(a^2+x^2)D[y[x],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*}