20.8.5 problem Problem 5

Internal problem ID [3738]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial Solutions. page 529
Problem number : Problem 5
Date solved : Sunday, March 30, 2025 at 02:06:56 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=40 \sin \left (x \right )^{2} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-2*y(x) = 40*sin(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} c_2 +{\mathrm e}^{2 x} c_1 -10+\sin \left (2 x \right )+3 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 0.07 (sec). Leaf size: 33

ode=D[y[x],{x,2}]-D[y[x],x]-2*y[x]==40*Sin[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sin (2 x)+3 \cos (2 x)+c_1 e^{-x}+c_2 e^{2 x}-10 \]

✓ Sympy. Time used: 0.587 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) - 40*sin(x)**2 - Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{2 x} + \sin {\left (2 x \right )} + 3 \cos {\left (2 x \right )} - 10 \]