60.1.191 problem 192

Internal problem ID [10205]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 192
Date solved : Monday, January 27, 2025 at 06:38:20 PM
CAS classification : [_linear]

\begin{align*} \sqrt {a^{2}+x^{2}}\, y^{\prime }+y-\sqrt {a^{2}+x^{2}}+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (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)
 

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

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 42

DSolve[Sqrt[x^2+a^2]*D[y[x],x] + y[x] - Sqrt[x^2+a^2] + x==0,y[x],x,IncludeSingularSolutions -> True]
 

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