88.14.7 problem 7

Internal problem ID [24095]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 93
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:59:11 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 36

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 47

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

\begin{align*} y(x)&\to e^{-\frac {1}{2} x \left (\sqrt {k^2-4 L}+k\right )} \left (c_2 e^{x \sqrt {k^2-4 L}}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 39

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

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