60.5.25 problem 1560

Internal problem ID [11559]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1560
Date solved : Monday, January 27, 2025 at 11:23:28 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = c_{1} +c_{2} \ln \left (x \right )+\frac {c_3}{x}+c_4 x \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 29

DSolve[6*x*D[y[x],{x,2}] + 6*x^2*Derivative[3][y][x] + x^3*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{2 x}+c_4 x-c_2 \log (x)+c_2+c_3 \]