Internal problem ID [2230]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear
Differential Equations. page 502
Problem number: Problem 37.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(x^3*diff(y(x),x$3)+3*x^2*diff(y(x),x$2)-6*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} x^{\sqrt {7}}+c_{3} x^{-\sqrt {7}} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 40
DSolve[x^3*y'''[x]+3*x^2*y''[x]-6*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^{-\sqrt {7}} \left (c_2 x^{2 \sqrt {7}}-c_1\right )}{\sqrt {7}}+c_3 \\ \end{align*}