Internal problem ID [9155]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1576.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {f \left (y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y\right )+2 \mathit {df} \left (-a^{2} y^{\prime }+y^{\prime \prime \prime }\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 67
dsolve(f*(diff(diff(diff(diff(y(x),x),x),x),x)-2*a^2*diff(diff(y(x),x),x)+a^4*y(x))+2*df*(diff(diff(diff(y(x),x),x),x)-a^2*diff(y(x),x))=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-a x}+c_{2} {\mathrm e}^{a x}+c_{3} {\mathrm e}^{\frac {\left (-\mathit {df} +\sqrt {a^{2} f^{2}+\mathit {df}^{2}}\right ) x}{f}}+c_{4} {\mathrm e}^{-\frac {\left (\mathit {df} +\sqrt {a^{2} f^{2}+\mathit {df}^{2}}\right ) x}{f}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2*Derivative[1][f][x]*(-(a^2*y'[x]) + Derivative[3][y][x]) + f[x]*(a^4*y[x] - 2*a^2*y''[x] + Derivative[4][y][x]) == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved