56.1.41 problem 41

Internal problem ID [8753]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 41
Date solved : Wednesday, March 05, 2025 at 06:44:18 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime }+2 y^{\prime }+4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 20

ode:=5*diff(diff(y(x),x),x)+2*diff(y(x),x)+4*y(x) = 0; 
ic:=y(0) = 0, D(y)(0) = 5; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {25 \sqrt {19}\, {\mathrm e}^{-\frac {x}{5}} \sin \left (\frac {\sqrt {19}\, x}{5}\right )}{19} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 6

ode=5*D[y[x],{x,2}]+2*D[y[x],x]+4*y[x]==0; 
ic={y[0]==0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 0 \]

✓ Sympy. Time used: 0.205 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + 2*Derivative(y(x), x) + 5*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {25 \sqrt {19} e^{- \frac {x}{5}} \sin {\left (\frac {\sqrt {19} x}{5} \right )}}{19} \]