Internal problem ID [6786]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 97. The p-discriminant equation.
EXERCISES Page 314
Problem number: 8.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x {y^{\prime }}^{2}-2 y^{\prime } y=-4 x} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 29
dsolve(x*diff(y(x),x)^2-2*y(x)*diff(y(x),x)+4*x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -2 x y \left (x \right ) = 2 x y \left (x \right ) = -\frac {\left (-\frac {x^{2}}{c_{1}^{2}}-4\right ) c_{1}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.294 (sec). Leaf size: 43
DSolve[x*(y'[x])^2-2*y[x]*y'[x]+4*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x \cosh (-\log (x)+c_1) y(x)\to -2 x \cosh (\log (x)+c_1) y(x)\to -2 x y(x)\to 2 x \end{align*}