Internal problem ID [9892]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1560.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x^3*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^2*diff(diff(diff(y(x),x),x),x)+6*x*diff(diff(y(x),x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} \ln \left (x \right )+\frac {c_{3}}{x}+c_{4} x \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 27
DSolve[6*x*y''[x] + 6*x^2*Derivative[3][y][x] + x^3*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1}{2 x}+c_4 x-c_2 \log (x)+c_3 \]