85.33.56 problem 56

Internal problem ID [22679]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 56
Date solved : Thursday, October 02, 2025 at 09:06:18 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} i^{\prime }+3 i&=10 \sin \left (t \right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 17

ode:=diff(i(t),t)+3*i(t) = 10*sin(t); 
ic:=[i(0) = 0]; 
dsolve([ode,op(ic)],i(t), singsol=all);
 

\[ i = -\cos \left (t \right )+3 \sin \left (t \right )+{\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 19

ode=D[i[t],t]+3*i[t]==10*Sin[t]; 
ic={i[0]==0}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to e^{-3 t}+3 \sin (t)-\cos (t) \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
i = Function("i") 
ode = Eq(3*i(t) - 10*sin(t) + Derivative(i(t), t),0) 
ics = {i(0): 0} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = 3 \sin {\left (t \right )} - \cos {\left (t \right )} + e^{- 3 t} \]