8.4.2 problem 2

Internal problem ID [705]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 2
Date solved : Tuesday, March 04, 2025 at 11:33:21 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 11

ode:=-2*y(x)+diff(y(x),x) = 3*exp(2*x); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 3 \,{\mathrm e}^{2 x} x \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 13

ode=-2*y[x]+D[y[x],x] == 3*Exp[2*x]; 
ic=y[0]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 3 e^{2 x} x \]

✓ Sympy. Time used: 0.143 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = 3 x e^{2 x} \]