56.1.88 problem 87

Internal problem ID [8800]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 87
Date solved : Sunday, March 30, 2025 at 01:40:03 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.065 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+diff(y(x),x)+y(x) = 0; 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 26

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

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

✓ Sympy. Time used: 0.147 (sec). Leaf size: 19

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

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