Internal problem ID [6088]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x^{2}-3=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 16
dsolve(x^3*diff(y(x),x$2)-x^2*diff(y(x),x)=3-x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{2}}{2}+\frac {1}{x}+x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 21
DSolve[x^3*y''[x]-x^2*y'[x]==3-x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 x^2}{2}+x+\frac {1}{x}+c_2 \\ \end{align*}