Internal problem ID [6100]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES
Page 324
Problem number: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime } \left (2-3 x y^{\prime }\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.044 (sec). Leaf size: 16
dsolve(x*diff(y(x),x$2)=diff(y(x),x)*(2-3*x*diff(y(x),x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (x^{3} c_{1}+3 c_{2}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.196 (sec). Leaf size: 19
DSolve[x*y''[x]==y'[x]*(2-3*x*y'[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \log \left (x^3+c_1\right )+c_2 \\ \end{align*}