Internal problem ID [3420]
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]
\[ \boxed {x y^{\prime }-y \left (y+1\right )=x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 10
dsolve(x*diff(y(x),x) = x^2+y(x)*(1+y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (x +c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.191 (sec). Leaf size: 12
DSolve[x y'[x]==x^2+y[x](1+y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \tan (x+c_1) \]