81.10.17 problem 14-17

Internal problem ID [21612]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 14. Second order homogeneous differential equations with constant coefficients. Page 297.
Problem number : 14-17
Date solved : Thursday, October 02, 2025 at 07:59:01 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ y^{\prime }\left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)+diff(y(x),x)-6*y(x) = 0; 
ic:=[y(0) = 4, D(y)(0) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 3 \,{\mathrm e}^{2 x}+{\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 48

ode=D[y[x],{x,2}]+D[y[x],x]+6*y[x]==0; 
ic={y[0]==4,Derivative[1][y][0] ==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2}{23} e^{-x/2} \left (5 \sqrt {23} \sin \left (\frac {\sqrt {23} x}{2}\right )+46 \cos \left (\frac {\sqrt {23} x}{2}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 4, Subs(Derivative(y(x), x), x, 0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\frac {10 \sqrt {23} \sin {\left (\frac {\sqrt {23} x}{2} \right )}}{23} + 4 \cos {\left (\frac {\sqrt {23} x}{2} \right )}\right ) e^{- \frac {x}{2}} \]