Internal problem ID [5122]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page
218
Problem number: Problem 3.1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y+\sqrt {x^{2}+y^{2}}-x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 27
dsolve(y(x)+sqrt(x^2+y(x)^2)-x*diff(y(x),x)=0,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: 7.72 (sec). Leaf size: 50
DSolve[y[x]+Sqrt[x^2+y[x]^2]-x*y'[x]==0,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*}