Internal problem ID [9135]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1556.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 19
dsolve(x^2*diff(diff(diff(diff(y(x),x),x),x),x)+8*x*diff(diff(diff(y(x),x),x),x)+12*diff(diff(y(x),x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+\frac {c_{2}}{x}+\frac {c_{3}}{x^{2}}+c_{4} x \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 27
DSolve[12*y''[x] + 8*x*Derivative[3][y][x] + x^2*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 c_2 x+c_1}{6 x^2}+c_4 x+c_3 \\ \end{align*}