Internal problem ID [955]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime } x -2 y-\frac {x^{6}}{x^{2}+y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 41
dsolve(x*diff(y(x),x)-2*y(x)=x^6/(y(x)+x^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-1-\sqrt {x^{2}-2 c_{1}+1}\right ) x^{2} \\ y \relax (x ) = \left (-1+\sqrt {x^{2}-2 c_{1}+1}\right ) x^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.637 (sec). Leaf size: 70
DSolve[x*y'[x]-2*y[x]==x^6/(y[x]+x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x^2 \left (1+\sqrt {\frac {1}{x^5}} x^2 \sqrt {x \left (x^2+1+c_1\right )}\right ) \\ y(x)\to -x^2+\sqrt {\frac {1}{x^5}} x^4 \sqrt {x \left (x^2+1+c_1\right )} \\ \end{align*}