Internal problem ID [2739]
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]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} +c_{2} x^{\sqrt {7}}+c_{3} x^{-\sqrt {7}} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 41
DSolve[x^3*y'''[x]+3*x^2*y''[x]-6*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {c_1 x^{-\sqrt {7}}}{\sqrt {7}}+\frac {c_2 x^{\sqrt {7}}}{\sqrt {7}}+c_3 \]