65.4.13 problem 13

Internal problem ID [15672]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:22:47 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=4 y-5 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 14

ode:=diff(y(x),x) = 4*y(x)-5; 
ic:=[y(1) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {5}{4}+\frac {11 \,{\mathrm e}^{-4+4 x}}{4} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 20

ode=D[y[x],x]==4*y[x]-5; 
ic={y[1]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {11}{4} e^{4 x-4}+\frac {5}{4} \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + Derivative(y(x), x) + 5,0) 
ics = {y(1): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {11 e^{4 x}}{4 e^{4}} + \frac {5}{4} \]