35.6.19 problem 19

Internal problem ID [6169]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 19
Date solved : Sunday, March 30, 2025 at 10:41:50 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+5 y&=40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

ode:=4*diff(diff(y(x),x),x)+4*diff(y(x),x)+5*y(x) = 40*exp(-3/2*x)*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (4 \cos \left (x \right )^{2}+\left ({\mathrm e}^{x} c_1 -2 \sin \left (x \right )\right ) \cos \left (x \right )+c_2 \sin \left (x \right ) {\mathrm e}^{x}-2\right ) {\mathrm e}^{-\frac {3 x}{2}} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 42

ode=4*D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==40*Exp[-3*x/2]*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.403 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) + 4*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)) - 40*exp(-3*x/2)*sin(2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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