35.6.12 problem 12

Internal problem ID [6162]
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 : 12
Date solved : Sunday, March 30, 2025 at 10:41:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+12 y&=80 \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 43

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+12*y(x) = 80*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} \sin \left (2 \sqrt {2}\, x \right ) c_2 +{\mathrm e}^{-2 x} \cos \left (2 \sqrt {2}\, x \right ) c_1 +5 \sin \left (2 x \right )-5 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 52

ode=D[y[x],{x,2}]+4*D[y[x],x]+12*y[x]==80*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 5 \sin (2 x)-5 \cos (2 x)+c_2 e^{-2 x} \cos \left (2 \sqrt {2} x\right )+c_1 e^{-2 x} \sin \left (2 \sqrt {2} x\right ) \]

✓ Sympy. Time used: 0.251 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) - 80*sin(2*x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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