Internal problem ID [947]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x +y y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (3) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 15
dsolve([x+y(x)*diff(y(x),x)=0,y(3) = -4],y(x), singsol=all)
\[ y \relax (x ) = -\sqrt {-x^{2}+25} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 18
DSolve[{x+y[x]*y'[x]==0,y[3]==-4},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {25-x^2} \\ \end{align*}