67.4.13 problem 5.2 (c)

Internal problem ID [16382]
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 (c)
Date solved : Thursday, October 02, 2025 at 01:27:16 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=4 y+16 x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x) = 4*y(x)+16*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -4 x -1+{\mathrm e}^{4 x} c_1 \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 31

ode=D[y[x],x]==4*y[x]+16*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{4 x} \left (\int _1^x16 e^{-4 K[1]} K[1]dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.068 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*x - 4*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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