85.49.1 problem 1 (a)

Internal problem ID [22802]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 194
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 09:14:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y&=2 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+y(x) = 2*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (x \right ) c_2 +\cos \left (x \right ) c_1 +\frac {{\mathrm e}^{3 x}}{5} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {e^{3 x}}{5}+c_1 \cos (x)+c_2 \sin (x) \end{align*}

✓ Sympy. Time used: 0.051 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )} + \frac {e^{3 x}}{5} \]