Internal problem ID [1058]
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: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 y}{x}+\frac {2 x y}{x^{2}+2 x^{2} y+1}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve([diff(y(x),x)+2/x*y(x)= -(2*x*y(x))/(x^2+2*x^2*y(x)+1),y(1) = -2],y(x), singsol=all)
\[ y \relax (x ) = \frac {-x^{2}-1}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.663 (sec). Leaf size: 39
DSolve[{y'[x]+2/x*y[x]== -(2*x*y[x])/(x^2+2*x^2*y[x]+1),y[1]==-2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-\frac {x^{3/2}+\sqrt {x^3 \left (x^2+1\right )^2}}{x^{7/2}}-1\right ) \\ \end{align*}