Internal problem ID [2670]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve(3*(x^2+y(x)^2)+x*(x^2+3*y(x)^2+6*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ c_{1}+{\mathrm e}^{y \relax (x )} \left (\frac {x^{3}}{3}+x y \relax (x )^{2}\right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 26
DSolve[3*(x^2+y[x]^2)+x*(x^2+3*y[x]^2+6*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^3 e^{y(x)}+3 x e^{y(x)} y(x)^2=c_1,y(x)\right ] \]