60.5.32 problem 1567

Internal problem ID [11566]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1567
Date solved : Monday, January 27, 2025 at 11:23:31 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+8*x^3*diff(diff(diff(y(x),x),x),x)+12*x^2*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: 0.023 (sec). Leaf size: 27

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

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