15.8.20 problem 20

Internal problem ID [3023]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 20
Date solved : Monday, January 27, 2025 at 07:09:06 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.312 (sec). Leaf size: 13

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

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