69.1.34 problem 52

Internal problem ID [14187]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 52
Date solved : Tuesday, January 28, 2025 at 06:19:47 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 32

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

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

✓ Solution by Mathematica

Time used: 0.228 (sec). Leaf size: 16

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

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