Internal problem ID [9098]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1519.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (x +2\right ) y^{\prime \prime }+6 \left (x +1\right ) y^{\prime }-6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 20
dsolve((x+3)*x^2*diff(diff(diff(y(x),x),x),x)-3*x*(x+2)*diff(diff(y(x),x),x)+6*(x+1)*diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2}+x^{3} c_{2}+c_{3} \left (x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 53
DSolve[-6*y[x] + 6*(1 + x)*y'[x] - 3*x*(2 + x)*y''[x] + x^2*(3 + x)*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} \left (-4 c_2 \left (x^3-3 x^2+x+1\right )+c_3 (3 x+1) (x-1)^2+2 c_1 (x ((x-3) x+3)+3)\right ) \\ \end{align*}