60.5.42 problem 1577

Internal problem ID [11576]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1577
Date solved : Monday, January 27, 2025 at 11:23:36 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} f y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(f*diff(diff(diff(diff(y(x),x),x),x),x)=0,y(x), singsol=all)
 

\[ y = \frac {1}{6} c_{1} x^{3}+\frac {1}{2} c_{2} x^{2}+x c_3 +c_4 \]

✓ Solution by Mathematica

Time used: 14.345 (sec). Leaf size: 41

DSolve[Derivative[2][f][x]*D[y[x],{x,2}] + 2*Derivative[1][f][x]*Derivative[3][y][x] + f[x]*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\int _1^{K[2]}\frac {c_1+c_2 K[1]}{f(K[1])}dK[1]dK[2]+c_4 x+c_3 \]