67.4.12 problem 5.2 (b)

Internal problem ID [16381]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.2 (b)
Date solved : Thursday, October 02, 2025 at 01:27:15 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} 2 y+y^{\prime }&=20 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(y(x),x)+2*y(x) = 20*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (4 \,{\mathrm e}^{5 x}+c_1 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 21

ode=D[y[x],x]+2*y[x]==20*Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (4 e^{5 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 20*exp(3*x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + 4 e^{3 x} \]