60.5.21 problem 1556

Internal problem ID [11555]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1556
Date solved : Monday, January 27, 2025 at 11:23:26 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = c_{1} +\frac {c_{2}}{x}+\frac {c_3}{x^{2}}+c_4 x \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 27

DSolve[12*D[y[x],{x,2}] + 8*x*Derivative[3][y][x] + x^2*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 c_2 x+c_1}{6 x^2}+c_4 x+c_3 \]