Internal problem ID [3612]
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]
\[ \boxed {x \left (x^{2}+1\right ) y^{\prime }+x^{2} y=a} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(x*(x^2+1)*diff(y(x),x) = a-x^2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-a \,\operatorname {arctanh}\left (\frac {1}{\sqrt {x^{2}+1}}\right )+c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 31
DSolve[x(1+x^2)y'[x]==a-x^2 y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-a \text {arctanh}\left (\sqrt {x^2+1}\right )+c_1}{\sqrt {x^2+1}} \]