85.52.1 problem 1

Internal problem ID [22812]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 195
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:14:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=4 \sin \left (3 x \right )^{3} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 4*sin(3*x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} c_1 +{\mathrm e}^{x} c_2 -\frac {27 \cos \left (9 x \right )}{6970}+\frac {27 \cos \left (3 x \right )}{130}+\frac {79 \sin \left (9 x \right )}{6970}-\frac {21 \sin \left (3 x \right )}{130} \]

✓ Mathematica. Time used: 0.161 (sec). Leaf size: 52

ode=D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==4*Sin[3*x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {21}{130} \sin (3 x)+\frac {79 \sin (9 x)}{6970}+\frac {27}{130} \cos (3 x)-\frac {27 \cos (9 x)}{6970}+c_1 e^x+c_2 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.587 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 4*sin(3*x)**3 - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{2 x} - \frac {21 \sin {\left (3 x \right )}}{130} + \frac {79 \sin {\left (9 x \right )}}{6970} + \frac {27 \cos {\left (3 x \right )}}{130} - \frac {27 \cos {\left (9 x \right )}}{6970} \]