26.3.8 problem 4(e)

Internal problem ID [4268]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 10, page 47
Problem number : 4(e)
Date solved : Monday, January 27, 2025 at 08:47:08 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} x y^{\prime }&=y+x^{2}+9 y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (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: 0.260 (sec). Leaf size: 17

DSolve[x*D[y[x],x]==y[x]+x^2+9*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} x \tan (3 (x+c_1)) \]