Internal problem ID [12162]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 92.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y-y {y^{\prime }}^{2}-2 x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 75
dsolve(y(x)=y(x)*diff(y(x),x)^2+2*x*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = -i x y \left (x \right ) = i x y \left (x \right ) = 0 y \left (x \right ) = \sqrt {c_{1}^{2}-2 c_{1} x} y \left (x \right ) = \sqrt {c_{1}^{2}+2 c_{1} x} y \left (x \right ) = -\sqrt {c_{1}^{2}-2 c_{1} x} y \left (x \right ) = -\sqrt {c_{1}^{2}+2 c_{1} x} \end{align*}
✓ Solution by Mathematica
Time used: 0.788 (sec). Leaf size: 126
DSolve[y[x]==y[x]*(y'[x])^2+2*x*y'[x],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 -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 y(x)\to -i x y(x)\to i x \end{align*}