74.13.37 problem 63 (b)

Internal problem ID [16403]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 63 (b)
Date solved : Tuesday, January 28, 2025 at 09:07:31 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ y^{\prime \prime }\left (0\right )&=-1\\ y^{\prime \prime \prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.070 (sec). Leaf size: 36

dsolve([diff(y(t),t$4)-8*diff(y(t),t$3)+30*diff(y(t),t$2)-56*diff(y(t),t)+49*y(t)=0,y(0) = 1, D(y)(0) = 2, (D@@2)(y)(0) = -1, (D@@3)(y)(0) = -1],y(t), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{2 t} \left (\left (\frac {21 t}{2}-3\right ) \cos \left (\sqrt {3}\, t \right )+\sin \left (\sqrt {3}\, t \right ) \sqrt {3}\, \left (t -\frac {7}{2}\right )\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 49

DSolve[{D[y[t],{t,4}]-8*D[ y[t],{t,3}]+30*D[y[t],{t,2}]-56*D[y[t],t]+49*y[t]==0,{y[0]==1,Derivative[1][y][0] ==2,Derivative[2][y][0] ==-1,Derivative[3][y][0]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {1}{6} e^{2 t} \left (\sqrt {3} (2 t-7) \sin \left (\sqrt {3} t\right )+3 (7 t-2) \cos \left (\sqrt {3} t\right )\right ) \]