Internal problem ID [2598]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 10, page 47
Problem number: 4(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Riccati]
\[ \boxed {y^{\prime } x -y-x^{2}-9 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve(x*diff(y(x),x)=y(x)+x^2+9*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\tan \left (3 x +3 c_{1} \right ) x}{3} \]
✓ Solution by Mathematica
Time used: 0.248 (sec). Leaf size: 17
DSolve[x*y'[x]==y[x]+x^2+9*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} x \tan (3 (x+c_1)) \\ \end{align*}