Internal problem ID [10214]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
28. Summary. Page 59
Problem number: Ex 4.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {3 x \left (y^{\prime }\right )^{2}-6 y^{\prime } y+x +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 40
dsolve(3*x*diff(y(x),x)^2-6*y(x)*diff(y(x),x)+x+2*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = x \\ y \relax (x ) = -\frac {x}{3} \\ y \relax (x ) = \frac {\left (-\frac {\left (x +c_{1}\right )^{2}}{3 c_{1}^{2}}-1\right ) x}{-\frac {2 \left (x +c_{1}\right )}{c_{1}}+2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.344 (sec). Leaf size: 67
DSolve[3*x*(y'[x])^2-6*y[x]*y'[x]+x+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (x-2 x \cosh \left (-\log (x)+\sqrt {3} c_1\right )\right ) \\ y(x)\to \frac {1}{3} \left (x-2 x \cosh \left (\log (x)+\sqrt {3} c_1\right )\right ) \\ y(x)\to -\frac {x}{3} \\ y(x)\to x \\ \end{align*}