8.5.13 problem 13

Internal problem ID [741]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 13
Date solved : Wednesday, February 05, 2025 at 03:57:14 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: 0.006 (sec). Leaf size: 26

dsolve(x*diff(y(x),x) = y(x)+(x^2+y(x)^2)^(1/2),y(x), singsol=all)
 

\[ \frac {-c_1 \,x^{2}+\sqrt {x^{2}+y^{2}}+y}{x^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.279 (sec). Leaf size: 13

DSolve[x*D[y[x],x] == y[x]+(x^2+y[x]^2)^(1/2),y[x],x,IncludeSingularSolutions -> True]
 

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