Internal problem ID [2181]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 42.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 y}{x}-6 x^{4} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 17
dsolve(diff(y(x),x)+2/x*y(x)=6*y(x)^2*x^4,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\left (-2 x^{3}+c_{1}\right ) x^{2}} \]
✓ Solution by Mathematica
Time used: 0.133 (sec). Leaf size: 24
DSolve[y'[x]+2/x*y[x]==6*y[x]^2*x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-2 x^5+c_1 x^2} \\ y(x)\to 0 \\ \end{align*}