Internal problem ID [12134]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 56.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y y^{\prime }-\sqrt {x^{2}+y^{2}}=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(y(x)*diff(y(x),x)=-x+sqrt(x^2+y(x)^2),y(x), singsol=all)
\[ -c_{1} +\frac {x}{y \left (x \right )^{2}}+\frac {\sqrt {y \left (x \right )^{2}+x^{2}}}{y \left (x \right )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.656 (sec). Leaf size: 57
DSolve[y[x]*y'[x]==-x+Sqrt[x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} y(x)\to 0 \end{align*}