Internal problem ID [9132]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1553.
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 }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 18
dsolve(x^2*diff(diff(diff(diff(y(x),x),x),x),x)+4*x*diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} \ln \relax (x )+c_{3} x +c_{4} x \ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 29
DSolve[2*y''[x] + 4*x*Derivative[3][y][x] + x^2*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (c_4-c_2) x+(c_2 x-c_1) \log (x)+c_3 \\ \end{align*}