Internal problem ID [9156]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1577.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _quadrature]]
Solve \begin {gather*} \boxed {f y^{\prime \prime \prime \prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(f*diff(diff(diff(diff(y(x),x),x),x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{6} c_{1} x^{3}+\frac {1}{2} c_{2} x^{2}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 41
DSolve[Derivative[2][f][x]*y''[x] + 2*Derivative[1][f][x]*Derivative[3][y][x] + f[x]*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 \\ \end{align*}