10.5.4 problem 4

Internal problem ID [1196]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 4
Date solved : Monday, January 27, 2025 at 04:43:50 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 31

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

\begin{align*} y &= -\frac {1}{x} \\ y &= \frac {-1-c_1}{x} \\ y &= \frac {c_1 -1}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 29

DSolve[2*y[x]+2*x*y[x]^2+(2*x+2*x^2*y[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*}