Internal problem ID [3104]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 356.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x \left (x^{2}+1\right ) y^{\prime }-a +y x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 25
dsolve(x*(x^2+1)*diff(y(x),x) = a-x^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {-a \arctanh \left (\frac {1}{\sqrt {x^{2}+1}}\right )+c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 31
DSolve[x(1+x^2)y'[x]==a-x^2 y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-a \tanh ^{-1}\left (\sqrt {x^2+1}\right )+c_1}{\sqrt {x^2+1}} \\ \end{align*}