4.10.1 problem 1

Internal problem ID [1333]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page 190
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 04:32:44 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t)-5*diff(y(t),t)+6*y(t) = 2*exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{t} \left ({\mathrm e}^{t} c_2 +c_1 \,{\mathrm e}^{2 t}+1\right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 25

ode=D[y[t],{t,2}]-5*D[y[t],t]+6*y[t] == 2*Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^t \left (c_1 e^t+c_2 e^{2 t}+1\right ) \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(6*y(t) - 2*exp(t) - 5*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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