12.18.25 problem section 9.2, problem 25

Internal problem ID [2139]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 25
Date solved : Monday, January 27, 2025 at 05:42:46 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=1\\ y^{\prime \prime \prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

dsolve([4*diff(y(x),x$4)-13*diff(y(x),x$2)+9*y(x)=0,y(0) = 1, D(y)(0) = 3, (D@@2)(y)(0) = 1, (D@@3)(y)(0) = 3],y(x), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{x}-{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 18

DSolve[{4*D[y[x],{x,4}]-13*D[y[x],{x,2}]+9*y[x]==0,{y[0]==1,Derivative[1][y][0] ==3,Derivative[2][y][0] ==1,Derivative[3][y][0]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 e^x-e^{-x} \]