86.10.7 problem 7

Internal problem ID [23187]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 9. The operational method. Exercise 9b at page 134
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:24:09 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-5 y&=2 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

ode:=2*diff(diff(y(x),x),x)-3*diff(y(x),x)-5*y(x) = 2*sin(2*x)+3*cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {5 x}{2}} c_2 +{\mathrm e}^{-x} c_1 -\frac {27 \cos \left (2 x \right )}{205}-\frac {44 \sin \left (2 x \right )}{205} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 52

ode=D[y[x],{x,2}]-3*D[y[x],x]-5*y[x]==2*Sin[2*x]+3*Cos[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {4}{13} \sin (2 x)-\frac {5}{39} \cos (2 x)+e^{-\frac {1}{2} \left (\sqrt {29}-3\right ) x} \left (c_2 e^{\sqrt {29} x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.175 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) - 2*sin(2*x) - 3*cos(2*x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (3 - \sqrt {29}\right )}{2}} + C_{2} e^{\frac {x \left (3 + \sqrt {29}\right )}{2}} - \frac {4 \sin {\left (2 x \right )}}{13} - \frac {5 \cos {\left (2 x \right )}}{39} \]