2.7.8 problem 8

Internal problem ID [814]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 04:15:40 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ y^{\prime }\left (0\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.043 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x) = 0; 
ic:=[y(0) = 4, D(y)(0) = -2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {14}{3}-\frac {2 \,{\mathrm e}^{3 x}}{3} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to -\frac {2}{3} \left (e^{3 x}-7\right ) \end{align*}

✓ Sympy. Time used: 0.084 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {14}{3} - \frac {2 e^{3 x}}{3} \]