Internal problem ID [7771]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 192.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\sqrt {a^{2}+x^{2}}\, y^{\prime }+y-\sqrt {a^{2}+x^{2}}+x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(sqrt(x^2+a^2)*diff(y(x),x) + y(x) - sqrt(x^2+a^2) + x=0,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: 8.199 (sec). Leaf size: 78
DSolve[Sqrt[x^2+a^2]*y'[x] + y[x] - Sqrt[x^2+a^2] + x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\sqrt {a^2+x^2}-x\right ) \text {arctanh}\left (\frac {x}{\sqrt {a^2+x^2}}\right )+\frac {c_1 \sqrt {1-\frac {x}{\sqrt {a^2+x^2}}}}{\sqrt {\frac {x}{\sqrt {a^2+x^2}}+1}} \\ \end{align*}