Internal problem ID [5121]
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]
\[ \boxed {y+\sqrt {y^{2}+x^{2}}-y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(y(x)+sqrt(x^2+y(x)^2)-x*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {y \left (x \right )}{x^{2}}+\frac {\sqrt {x^{2}+y \left (x \right )^{2}}}{x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.339 (sec). Leaf size: 27
DSolve[y[x]+Sqrt[x^2+y[x]^2]-x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-c_1} \left (-1+e^{2 c_1} x^2\right ) \\ \end{align*}