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 : Tuesday, March 04, 2025 at 11:55:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

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

ode:=diff(diff(y(x),x),x)+16*y(x) = exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.080 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) - exp(3*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (4 x \right )} + C_{2} \cos {\left (4 x \right )} + \frac {e^{3 x}}{25} \]