64.11.31 problem 31

Internal problem ID [13481]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 05:45:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=18 \,{\mathrm e}^{-2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 24

dsolve([diff(y(x),x$2)+4*diff(y(x),x)+13*y(x)=18*exp(-2*x),y(0) = 0, D(y)(0) = 4],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 28

DSolve[{D[y[x],{x,2}]+4*D[y[x],x]+13*y[x]==18*Exp[-2*x],{y[0]==0,Derivative[1][y][0] ==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{-2 x} (4 \sin (3 x)-6 \cos (3 x)+6) \]