Internal problem ID [1038]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 75
dsolve((3*x^2+2*x*y(x)+4*y(x)^2)+(x^2+8*x*y(x)+18*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-x^{2}+\sqrt {-15 x^{4}-36 x^{3}-16 x c_{1}-36 c_{1}}}{8 x +18} \\ y \relax (x ) = -\frac {x^{2}+\sqrt {-15 x^{4}-36 x^{3}-16 x c_{1}-36 c_{1}}}{2 \left (4 x +9\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.44 (sec). Leaf size: 84
DSolve[(3*x^2+2*x*y[x]+4*y[x]^2)+(x^2+8*x*y[x]+18*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2+\sqrt {-3 x^3 (5 x+12)+4 c_1 (4 x+9)}}{8 x+18} \\ y(x)\to \frac {-x^2+\sqrt {-3 x^3 (5 x+12)+4 c_1 (4 x+9)}}{8 x+18} \\ \end{align*}