71.14.5 problem 11

Internal problem ID [14539]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.3, page 255
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 06:43:07 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.764 (sec). Leaf size: 15

dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=0,y(0) = 0, D(y)(0) = 3],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 18

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

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