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]
Solve \begin {gather*} \boxed {y^{\prime } x -y-x^{2}-9 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 15
dsolve(x*diff(y(x),x)=y(x)+x^2+9*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (3 x +3 c_{1}\right ) x}{3} \]
✓ Solution by Mathematica
Time used: 0.262 (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*}