12.6.3 problem 3

Internal problem ID [1682]
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 : 3
Date solved : Monday, January 27, 2025 at 05:27:07 AM
CAS classification : [_quadrature]

\begin{align*} 14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve((14*x^2*y(x)^3)+(21*x^2*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: 0.025 (sec). Leaf size: 25

DSolve[(14*x^2*y[x]^3)+(21*x^2*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*}