Internal problem ID [12133]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 55.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y+\frac {x}{y^{\prime }}-\sqrt {x^{2}+y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(y(x)+x/diff(y(x),x)=sqrt(x^2+y(x)^2),y(x), singsol=all)
\[ \frac {y \left (x \right )}{x^{2}}+\frac {\sqrt {y \left (x \right )^{2}+x^{2}}}{x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.527 (sec). Leaf size: 27
DSolve[y[x]+x/y'[x]==Sqrt[x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-c_1} \left (x^2-e^{2 c_1}\right ) \]