Internal problem ID [91]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y-\sqrt {x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 27
dsolve(x*diff(y(x),x) = y(x)+(x^2+y(x)^2)^(1/2),y(x), singsol=all)
\[ \frac {y \relax (x )}{x^{2}}+\frac {\sqrt {x^{2}+y \relax (x )^{2}}}{x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 7.622 (sec). Leaf size: 50
DSolve[x*y'[x] == y[x]+(x^2+y[x]^2)^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x \tanh (\log (x)+c_1)}{\sqrt {\text {sech}^2(\log (x)+c_1)}} \\ y(x)\to \frac {x \tanh (\log (x)+c_1)}{\sqrt {\text {sech}^2(\log (x)+c_1)}} \\ \end{align*}