60.5.3 problem 1536

Internal problem ID [11537]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1536
Date solved : Monday, January 27, 2025 at 11:23:17 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 48

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

\[ y = c_{1} {\mathrm e}^{-i \left (-\lambda \right )^{{1}/{4}} x}+c_{2} {\mathrm e}^{i \left (-\lambda \right )^{{1}/{4}} x}+c_3 \,{\mathrm e}^{-\left (-\lambda \right )^{{1}/{4}} x}+c_4 \,{\mathrm e}^{\left (-\lambda \right )^{{1}/{4}} x} \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 76

DSolve[\[Lambda]*y[x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{(-1)^{3/4} \sqrt [4]{\lambda } x}+c_2 e^{-\sqrt [4]{-1} \sqrt [4]{\lambda } x}+c_3 e^{-(-1)^{3/4} \sqrt [4]{\lambda } x}+c_4 e^{\sqrt [4]{-1} \sqrt [4]{\lambda } x} \]