12.6.1 problem 1

Internal problem ID [1680]
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
Date solved : Monday, January 27, 2025 at 05:25:20 AM
CAS classification : [_separable]

\begin{align*} 6 x^{2} y^{2}+4 x^{3} y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (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 &= 0 \\ y &= -\frac {\sqrt {2}\, \sqrt {-c_1 x}}{2 x^{2}} \\ y &= \frac {\sqrt {2}\, \sqrt {-c_1 x}}{2 x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 23

DSolve[6*x^2*y[x]^2+4*x^3*y[x]*D[y[x],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*}