19.2.1 problem 1

Internal problem ID [3530]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.6, page 50
Problem number : 1
Date solved : Sunday, March 30, 2025 at 01:46:15 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = \left ({\mathrm e}^{x}+c_1 \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 15

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

\[ y(x)\to e^x \left (e^x+c_1\right ) \]

✓ Sympy. Time used: 0.115 (sec). Leaf size: 10

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

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