76.5.29 problem 30

Internal problem ID [17449]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 10:38:38 AM
CAS classification : [_separable]

\begin{align*} 5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve((5*x*y(x)^2+5*y(x))+(5*x^2*y(x)+5*x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {1}{x} \\ y &= \frac {-5-c_{1}}{5 x} \\ y &= \frac {-5+c_{1}}{5 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 29

DSolve[(5*x*y[x]^2+5*y[x])+(5*x^2*y[x]+5*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{x} \\ y(x)\to \frac {c_1}{x} \\ y(x)\to -\frac {1}{x} \\ \end{align*}