66.1.3 problem Problem 3

Internal problem ID [13850]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 3
Date solved : Tuesday, January 28, 2025 at 06:05:10 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \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),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.350 (sec). Leaf size: 13

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

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