2.11.24 problem 47

Internal problem ID [892]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 47
Date solved : Tuesday, September 30, 2025 at 04:19:09 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x)+2*y(x) = 4*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\left (-c_2 \,{\mathrm e}^{x}+c_1 -\frac {2 \,{\mathrm e}^{3 x}}{3}\right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 29

ode=D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==4*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 e^x}{3}+c_1 e^{-2 x}+c_2 e^{-x} \end{align*}

✓ Sympy. Time used: 0.133 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 4*exp(x) + 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{- x} + \frac {2 e^{x}}{3} \]