12.7.26 problem 27

Internal problem ID [1736]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 27
Date solved : Monday, January 27, 2025 at 05:33:51 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

dsolve((3*x^2*y(x)^2+2*y(x))+(2*x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {2}{\left (3 x +2 c_1 \right ) x} \]

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 25

DSolve[(3*x^2*y[x]^2+2*y[x])+(2*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2}{3 x^2+2 c_1 x} \\ y(x)\to 0 \\ \end{align*}