Internal problem ID [9899]
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]]
\[ \boxed {f \left (y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y\right )+2 \operatorname {df} \left (y^{\prime \prime \prime }-a^{2} y^{\prime }\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 67
dsolve(f*(diff(y(x),x$4)-2*a^2*diff(y(x),x$2)+a^4*y(x))+2*df*(diff(y(x),x$3)-a^2*diff(y(x),x))=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{a x}+c_{2} {\mathrm e}^{-a x}+c_{3} {\mathrm e}^{\frac {\left (-\operatorname {df} +\sqrt {a^{2} f^{2}+\operatorname {df}^{2}}\right ) x}{f}}+c_{4} {\mathrm e}^{-\frac {\left (\operatorname {df} +\sqrt {a^{2} f^{2}+\operatorname {df}^{2}}\right ) x}{f}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 80
DSolve[f*(y''''[x]-2*a^2*y''[x]+a^4*y[x])+2*df*(y'''[x]-a^2*y'[x])==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{\frac {x \left (\sqrt {a^2 f^2+\text {df}^2}-\text {df}\right )}{f}}+c_2 e^{-\frac {x \left (\sqrt {a^2 f^2+\text {df}^2}+\text {df}\right )}{f}}+c_3 e^{-a x}+c_4 e^{a x} \]