78.12.7 problem 1 (g)

Internal problem ID [18215]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 1 (g)
Date solved : Thursday, March 13, 2025 at 11:49:15 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }+3 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 28

ode:=2*diff(diff(y(x),x),x)+2*diff(y(x),x)+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 42

ode=2*D[y[x],{x,2}] +2*D[y[x],x]+3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.169 (sec). Leaf size: 31

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

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