12.6.5 problem 5

Internal problem ID [1684]
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 : 5
Date solved : Monday, January 27, 2025 at 05:27:10 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 47

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

\begin{align*} y &= -x \\ y &= -x +c_1 \\ y &= -\frac {c_1}{2}-\frac {i \sqrt {3}\, c_1}{2}-x \\ y &= -\frac {c_1}{2}+\frac {i \sqrt {3}\, c_1}{2}-x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 18

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

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