12.7.21 problem 22

Internal problem ID [1731]
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 : 22
Date solved : Monday, January 27, 2025 at 05:33:38 AM
CAS classification : [_separable]

\begin{align*} x^{4} y^{4}+x^{5} y^{3} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve((x^4*y(x)^4)+(x^5*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= \frac {c_1}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 21

DSolve[(x^4*y[x]^4)+(x^5*y[x]^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 0 \\ y(x)\to \frac {c_1}{x} \\ y(x)\to 0 \\ \end{align*}