50.3.1 problem 1

Internal problem ID [10145]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 07:05:10 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

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

\[ y = \left (c_1 \,{\mathrm e}^{x \sqrt {c^{2}-4 k}}+c_2 \right ) {\mathrm e}^{-\frac {\left (c +\sqrt {c^{2}-4 k}\right ) x}{2}} \]

✓ Mathematica. Time used: 5.051 (sec). Leaf size: 2548

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

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✓ Sympy. Time used: 0.141 (sec). Leaf size: 39

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (- c + \sqrt {c^{2} - 4 k}\right )}{2}} + C_{2} e^{- \frac {x \left (c + \sqrt {c^{2} - 4 k}\right )}{2}} \]