Internal problem ID [3038]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 290.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }-2 x \left (x^{2}+1\right )^{2}-2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve((x^2+1)*diff(y(x),x) = 2*x*(x^2+1)^2+2*x*y(x),y(x), singsol=all)
\[ y \relax (x ) = \left (x^{2}+c_{1}\right ) \left (x^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 17
DSolve[(1+x^2)y'[x]==2 x(1+x^2)^2+2 x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (x^2+1\right ) \left (x^2+c_1\right ) \\ \end{align*}