Internal problem ID [581]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {x +y+\left (x +2 y\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 19
dsolve([x+y(x)+(x+2*y(x))*diff(y(x),x) = 0,y(2) = 3],y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{2}+\frac {\sqrt {-x^{2}+68}}{2} \]
✓ Solution by Mathematica
Time used: 0.512 (sec). Leaf size: 24
DSolve[{x+y[x]+(x+2*y[x])*y'[x] == 0,y[2]==3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\sqrt {68-x^2}-x\right ) \\ \end{align*}