Internal problem ID [6099]
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: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-y^{\prime } \left (3 x -2 y^{\prime }\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.052 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)=diff(y(x),x)*(3*x-2*diff(y(x),x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{2}+\frac {c_{1} \ln \left (x^{2}-c_{1}\right )}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.713 (sec). Leaf size: 28
DSolve[x^2*y''[x]==y'[x]*(3*x-2*y'[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x^2-c_1 \log \left (x^2+c_1\right )+2 c_2\right ) \\ \end{align*}