39.2.2 problem Problem 11.45

Internal problem ID [6519]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary Problems. page 101
Problem number : Problem 11.45
Date solved : Wednesday, March 05, 2025 at 12:55:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

\[ y = 4 \,{\mathrm e}^{2 x}+\left (c_1 x +c_2 \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 21

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

\[ y(x)\to e^x \left (4 e^x+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.189 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x + 4 e^{x}\right ) e^{x} \]