Internal problem ID [3646]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 392.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } \sqrt {a^{2}+x^{2}}+y=-x +\sqrt {a^{2}+x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (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: 8.172 (sec). Leaf size: 103
DSolve[y'[x] Sqrt[a^2+x^2]+x+y[x]==Sqrt[a^2 + x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (x-\sqrt {a^2+x^2}\right ) \left (\log \left (1-\frac {x}{\sqrt {a^2+x^2}}\right )-\log \left (\frac {x}{\sqrt {a^2+x^2}}+1\right )\right )+\frac {c_1 \sqrt {1-\frac {x}{\sqrt {a^2+x^2}}}}{\sqrt {\frac {x}{\sqrt {a^2+x^2}}+1}} \]