90.14.18 problem 27

Internal problem ID [25246]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 243
Problem number : 27
Date solved : Thursday, October 02, 2025 at 11:59:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y&=10 \,{\mathrm e}^{2 t} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t)+y(t) = 10*exp(2*t); 
ic:=[y(0) = 0, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -4 \sin \left (t \right )-2 \cos \left (t \right )+2 \,{\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 21

ode=D[y[t],{t,2}]+y[t]==10*Exp[2*t]; 
ic={y[0]==0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -2 \left (-e^{2 t}+2 \sin (t)+\cos (t)\right ) \end{align*}

✓ Sympy. Time used: 0.053 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 10*exp(2*t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 e^{2 t} - 4 \sin {\left (t \right )} - 2 \cos {\left (t \right )} \]