73.14.2 problem 21.5 (ii)

Internal problem ID [15412]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.5 (ii)
Date solved : Tuesday, January 28, 2025 at 07:54:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y&=24 \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 23

dsolve([diff(y(x),x$2)+4*y(x)=24*exp(2*x),y(0) = -2, D(y)(0) = 2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 25

DSolve[{D[y[x],{x,2}]+4*y[x]==24*Exp[2*x],{y[0]==-2,Derivative[1][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 e^{2 x}-2 \sin (2 x)-5 \cos (2 x) \]