Internal problem ID [2960]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 212.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime } x -\left (y^{2}+1\right ) \left (x^{2}+\arctan \relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 12
dsolve(x*diff(y(x),x) = (1+y(x)^2)*(x^2+arctan(y(x))),y(x), singsol=all)
\[ y \relax (x ) = \tan \left (c_{1} x +x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.3 (sec). Leaf size: 14
DSolve[x y'[x]==(1+y[x]^2)(x^2+ArcTan[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan (x (x+2 c_1)) \\ \end{align*}