Internal problem ID [3037]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 289.
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 -y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 19
dsolve((x^2+1)*diff(y(x),x) = 2*x*(x-y(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {2 x^{3}}{3}+c_{1}}{x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 25
DSolve[(1+x^2)y'[x]==2 x(x-y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x^3+3 c_1}{3 x^2+3} \\ \end{align*}