Internal problem ID [139]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {3 y^{2} x^{5}+y^{\prime } x^{3}-2 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(3*x^5*y(x)^2+x^3*diff(y(x),x) = 2*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{x^{5}+c_{1} x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.146 (sec). Leaf size: 28
DSolve[3*x^5*y[x]^2+x^3*y'[x] == 2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{x^5-c_1 x^2+1} \\ y(x)\to 0 \\ \end{align*}