Internal problem ID [3536]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 280.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }+y x=-a} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve((x^2+1)*diff(y(x),x)+a+x*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-a \,\operatorname {arcsinh}\left (x \right )+c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 34
DSolve[(1+x^2)y'[x]+a+x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {a \log \left (\sqrt {x^2+1}-x\right )+c_1}{\sqrt {x^2+1}} \]