71.14.4 problem 10

Internal problem ID [14538]
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 : 10
Date solved : Tuesday, January 28, 2025 at 06:43:07 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+9 y&=18 \,{\mathrm e}^{3 x} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 9.623 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)+9*y(x)=18*exp(3*x),y(0) = -1, D(y)(0) = 6],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 21

DSolve[{D[y[x],{x,2}]+9*y[x]==18*Exp[3*x],{y[0]==-1,Derivative[1][y][0] ==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x}+\sin (3 x)-2 \cos (3 x) \]