Internal problem ID [92]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x +y y^{\prime }-\sqrt {x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 28
dsolve(x+y(x)*diff(y(x),x) = (x^2+y(x)^2)^(1/2),y(x), singsol=all)
\[ -c_{1}+\frac {\sqrt {x^{2}+y \relax (x )^{2}}}{y \relax (x )^{2}}+\frac {x}{y \relax (x )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.398 (sec). Leaf size: 57
DSolve[x+y[x]*y'[x] == (x^2+y[x]^2)^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to 0 \\ \end{align*}