Internal problem ID [12451]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {\frac {y-y^{\prime } x}{\sqrt {x^{2}+y^{2}}}=m} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve((y(x)-x*diff(y(x),x))/sqrt(x^2+y(x)^2)=m,y(x), singsol=all)
\[ \frac {x^{m} y \left (x \right )+x^{m} \sqrt {y \left (x \right )^{2}+x^{2}}-c_{1} x}{x} = 0 \]
✓ Solution by Mathematica
Time used: 0.442 (sec). Leaf size: 36
DSolve[(y[x]-x*y'[x])/Sqrt[x^2+y[x]^2]==m,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-c_1} x^{1-m} \left (-x^{2 m}+e^{2 c_1}\right ) \]