59.1.505 problem 521

Internal problem ID [9677]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 521
Date solved : Sunday, March 30, 2025 at 02:44:07 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \end{align*}

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

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {3 x}{2}} \left (c_1 \sin \left (\frac {\sqrt {7}\, x}{2}\right )+c_2 \cos \left (\frac {\sqrt {7}\, x}{2}\right )\right ) \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 42

ode=D[y[x],{x,2}]+3*D[y[x],x]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x/2} \left (c_2 \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {7} x}{2}\right )\right ) \]

✓ Sympy. Time used: 0.173 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (\frac {\sqrt {7} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {7} x}{2} \right )}\right ) e^{- \frac {3 x}{2}} \]