71.12.1 problem 1

Internal problem ID [14517]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.5, page 221
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 06:42:54 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=5\\ y^{\prime \prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 23

dsolve([diff(y(x),x$3)-3*diff(y(x),x$2)-4*diff(y(x),x)+12*y(x)=0,y(0) = 1, D(y)(0) = 5, (D@@2)(y)(0) = -1],y(x), singsol=all)
 

\[ y = \left (-{\mathrm e}^{5 x}+3 \,{\mathrm e}^{4 x}-1\right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 26

DSolve[{D[y[x],{x,3}]-3*D[y[x],{x,2}]-4*D[y[x],x]+12*y[x]==0,{y[0]==1,Derivative[1][y][0] ==5,Derivative[2][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -e^{-2 x} \left (-3 e^{4 x}+e^{5 x}+1\right ) \]