8.11.1 problem 1

Internal problem ID [869]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 1
Date solved : Wednesday, February 05, 2025 at 04:42:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+16 y&={\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)+16*y(x)=exp(3*x),y(x), singsol=all)
 

\[ y = \sin \left (4 x \right ) c_2 +\cos \left (4 x \right ) c_1 +\frac {{\mathrm e}^{3 x}}{25} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]+16*y[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{3 x}}{25}+c_1 \cos (4 x)+c_2 \sin (4 x) \]