Internal problem ID [1027]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 52.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 y}{x}-\frac {3 x^{2} y^{2}+6 y x +2}{x^{2} \left (2 y x +3\right )}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 18
dsolve([diff(y(x),x)+2/x*y(x)=(3*x^2*y(x)^2+6*x*y(x)+2)/(x^2*(2*x*y(x)+3)),y(2) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {-3+\sqrt {60 x +1}}{2 x} \]
✓ Solution by Mathematica
Time used: 0.689 (sec). Leaf size: 35
DSolve[{y'[x]+2/x*y[x]==(3*x^2*y[x]^2+6*x*y[x]+2)/(x^2*(2*x*y[x]+3)),y[2]==2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {\frac {1}{x^2}} \sqrt {x^2 (60 x+1)}-3}{2 x} \\ \end{align*}