74.1.59 problem 81

Internal problem ID [15839]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 81
Date solved : Tuesday, January 28, 2025 at 08:09:15 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=-1\\ y^{\prime \prime \prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.101 (sec). Leaf size: 41

dsolve([diff(y(x),x$4)+25/2*diff(y(x),x$2)-5*diff(y(x),x)+629/16*y(x)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = -1, (D@@3)(y)(0) = 1],y(x), singsol=all)
 

\[ y = \frac {\left (74 \cos \left (3 x \right )+20 \sin \left (3 x \right )\right ) {\mathrm e}^{-\frac {x}{2}}}{208}-\frac {37 \,{\mathrm e}^{\frac {x}{2}} \left (\cos \left (2 x \right )-\frac {3 \sin \left (2 x \right )}{2}\right )}{104} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 47

DSolve[{D[y[x],{x,4}]+25/2*D[y[x],{x,2}]-5*D[y[x],x]+629/16*y[x]==0,{y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==-1,Derivative[3][y][0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{208} e^{-x/2} \left (111 e^x \sin (2 x)+20 \sin (3 x)-74 e^x \cos (2 x)+74 \cos (3 x)\right ) \]