Internal problem ID [2912]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 164.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -x^{2}-y \left (1+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 10
dsolve(x*diff(y(x),x) = x^2+y(x)*(1+y(x)),y(x), singsol=all)
\[ y \relax (x ) = \tan \left (c_{1}+x \right ) x \]
✓ Solution by Mathematica
Time used: 0.189 (sec). Leaf size: 12
DSolve[x y'[x]==x^2+y[x](1+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan (x+c_1) \\ \end{align*}