Internal problem ID [1034]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (x +y\right )^{2}+\left (x +y\right )^{2} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 49
dsolve((x+y(x))^2+(x+y(x))^2*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x \\ y \relax (x ) = c_{1}-x \\ y \relax (x ) = -\frac {c_{1}}{2}-\frac {i \sqrt {3}\, c_{1}}{2}-x \\ y \relax (x ) = -\frac {c_{1}}{2}+\frac {i \sqrt {3}\, c_{1}}{2}-x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[(x+y[x])^2+(x+y[x])^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \\ y(x)\to -x+c_1 \\ \end{align*}