Internal problem ID [9123]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1544.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+10 f y^{\prime \prime }+10 \mathit {df} y^{\prime }+\left (3 f^{2}+3 \mathit {ddf} \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+10*f*diff(diff(y(x),x),x)+10*df*diff(y(x),x)+(3*f^2+3*ddf)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+10 f \,\textit {\_Z}^{2}+10 \mathit {df} \textit {\_Z} +3 f^{2}+3 \mathit {ddf} , \mathit {index} =\textit {\_a} \right ) x} \textit {\_C}_{\textit {\_a}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[10*Derivative[1][f][x]*y'[x] + y[x]*(3*f[x]^2 + 3*Derivative[2][f][x]) + 10*f[x]*y''[x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved