77.1.122 problem 149 (page 224)

Internal problem ID [18012]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 149 (page 224)
Date solved : Tuesday, January 28, 2025 at 11:19:56 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x$4)+4*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \sin \left (x \right ) {\mathrm e}^{-x}+c_{2} {\mathrm e}^{-x} \cos \left (x \right )+c_{3} {\mathrm e}^{x} \sin \left (x \right )+c_4 \,{\mathrm e}^{x} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 40

DSolve[D[y[x],{x,4}]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\left (c_4 e^{2 x}+c_1\right ) \cos (x)+\left (c_3 e^{2 x}+c_2\right ) \sin (x)\right ) \]