48.4.1 problem Problem 3.1

Internal problem ID [7543]
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
Date solved : Monday, January 27, 2025 at 03:05:00 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y+\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 26

dsolve(y(x)+sqrt(x^2+y(x)^2)-x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \frac {-c_{1} x^{2}+y+\sqrt {x^{2}+y^{2}}}{x^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.321 (sec). Leaf size: 13

DSolve[y[x]+Sqrt[x^2+y[x]^2]-x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \sinh (\log (x)+c_1) \]