67.3.42 problem 4.8 (a)

Internal problem ID [16363]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.8 (a)
Date solved : Thursday, October 02, 2025 at 01:22:36 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-2 y&=-10 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=8 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 12

ode:=diff(y(x),x)-2*y(x) = -10; 
ic:=[y(0) = 8]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 5+3 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 14

ode=D[y[x],x]-2*y[x]==-10; 
ic={y[0]==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 e^{2 x}+5 \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) + Derivative(y(x), x) + 10,0) 
ics = {y(0): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 e^{2 x} + 5 \]