67.1.23 problem 2.4 (a)

Internal problem ID [16288]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.4 (a)
Date solved : Thursday, October 02, 2025 at 10:45:23 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=40 x \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 16

ode:=diff(y(x),x) = 40*x*exp(2*x); 
ic:=[y(0) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 14+\left (20 x -10\right ) {\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 24

ode=D[y[x],x]==4*x*10*Exp[2*x]; 
ic={y[0]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _0^x40 e^{2 K[1]} K[1]dK[1]+4 \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-40*x*exp(2*x) + Derivative(y(x), x),0) 
ics = {y(0): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 20 x e^{2 x} - 10 e^{2 x} + 14 \]