73.12.16 problem 19.3 (d)

Internal problem ID [15368]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.3 (d)
Date solved : Tuesday, January 28, 2025 at 07:53:50 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+9 y^{\prime \prime }+9 y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=10\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=6\\ y^{\prime \prime \prime }\left (0\right )&=-60 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 18

dsolve([diff(y(x),x$4)+diff(y(x),x$3)+9*diff(y(x),x$2)+9*diff(y(x),x)=0,y(0) = 10, D(y)(0) = 0, (D@@2)(y)(0) = 6, (D@@3)(y)(0) = -60],y(x), singsol=all)
 

\[ y = 4+6 \,{\mathrm e}^{-x}+2 \sin \left (3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.153 (sec). Leaf size: 55

DSolve[{D[y[x],{x,4}]+D[y[x],{x,3}]+9*D[y[x],{x,2}]+9*D[y[x],x]==0,{y[0]==10,Derivative[1][y][0] ==0,Derivative[2][y][0] ==6,Derivative[3][y][0]==-60}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\left (6 \cos (3 K[1])-6 e^{-K[1]}\right )dK[1]-\int _1^0\left (6 \cos (3 K[1])-6 e^{-K[1]}\right )dK[1]+10 \]