84.20.9 problem 12.17

Internal problem ID [22225]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 12. Second order linear homogeneous differential equations with constant coefficients. Supplementary problems
Problem number : 12.17
Date solved : Thursday, October 02, 2025 at 08:36:26 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-5 y&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{x \sqrt {29}}+c_2 \right ) {\mathrm e}^{-\frac {\left (-3+\sqrt {29}\right ) x}{2}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 35

ode=D[y[x],{x,2}]-3*D[y[x],x]-5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-\frac {1}{2} \left (\sqrt {29}-3\right ) x} \left (c_2 e^{\sqrt {29} x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (3 - \sqrt {29}\right )}{2}} + C_{2} e^{\frac {x \left (3 + \sqrt {29}\right )}{2}} \]