12.7.5 problem 5

Internal problem ID [1715]
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 : 5
Date solved : Monday, January 27, 2025 at 05:32:15 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

\begin{align*} y &= 0 \\ y &= c_1 \,{\mathrm e}^{-\frac {2 x}{3}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 25

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

\begin{align*} y(x)\to 0 \\ y(x)\to c_1 e^{-2 x/3} \\ y(x)\to 0 \\ \end{align*}