Internal problem ID [1030]
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: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {6 x^{2} y^{2}+4 y^{\prime } y x^{3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(6*x^2*y(x)^2+4*x^3*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= -\frac {\sqrt {2}\, \sqrt {-c_{1} x}}{2 x^{2}} \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {-c_{1} x}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 23
DSolve[6*x^2*y[x]^2+4*x^3*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to \frac {c_1}{x^{3/2}} \\ y(x)\to 0 \\ \end{align*}