Internal problem ID [11722]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page
113
Problem number: 13.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve(x^3*diff(y(x),x$3)-4*x^2*diff(y(x),x$2)+8*x*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \left (c_{1} x^{3}+c_{3} x +c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[x^3*y'''[x]-4*x^2*y''[x]+8*x*y'[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (c_3 x^3+c_2 x+c_1\right ) \]