Internal problem ID [10574]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, section 1.3. Exercises page 22
Problem number: 5.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 0, y^{\prime }\left (2\right ) = 2, y^{\prime \prime }\left (2\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)+6*x*diff(y(x),x)-6*y(x)=0,y(2) = 0, D(y)(2) = 2, (D@@2)(y)(2) = 6],y(x), singsol=all)
\[ y \left (x \right ) = x^{3}-3 x^{2}+2 x \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 13
DSolve[{x^3*y'''[x]-3*x^2*y''[x]+6*x*y'[x]-6*y[x]==0,{y[2]==0,y'[2]==2,y''[2]==6}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x-2) (x-1) x \\ \end{align*}