29.14.11 problem 392

Internal problem ID [4990]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 392
Date solved : Monday, January 27, 2025 at 10:01:29 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 42

DSolve[D[y[x],x] Sqrt[a^2+x^2]+x+y[x]==Sqrt[a^2 + x^2],y[x],x,IncludeSingularSolutions -> True]
 

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