60.5.18 problem 1553

Internal problem ID [11552]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1553
Date solved : Monday, January 27, 2025 at 11:23:25 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 29

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

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