10.6.17 problem 17

Internal problem ID [1234]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 17
Date solved : Saturday, March 29, 2025 at 10:49:23 PM
CAS classification : [[_linear, `class A`]]

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

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

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

\[ y = -{\mathrm e}^{2 x}+{\mathrm e}^{3 x} c_1 \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 19

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

\[ y(x)\to e^{2 x} \left (-1+c_1 e^x\right ) \]

✓ Sympy. Time used: 0.131 (sec). Leaf size: 14

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

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