34.4.4 problem 19 (e)

Internal problem ID [7931]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (e)
Date solved : Tuesday, September 30, 2025 at 05:10:15 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} i^{\prime }-6 i&=10 \sin \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(i(t),t)-6*i(t) = 10*sin(2*t); 
dsolve(ode,i(t), singsol=all);
 

\[ i = -\frac {\cos \left (2 t \right )}{2}-\frac {3 \sin \left (2 t \right )}{2}+{\mathrm e}^{6 t} c_1 \]

✓ Mathematica. Time used: 0.061 (sec). Leaf size: 34

ode=D[i[t],t]-6*i[t]==10*Sin[2*t]; 
ic={}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to e^{6 t} \left (\int _1^t10 e^{-6 K[1]} \sin (2 K[1])dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
i = Function("i") 
ode = Eq(-6*i(t) - 10*sin(2*t) + Derivative(i(t), t),0) 
ics = {} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = C_{1} e^{6 t} - \frac {3 \sin {\left (2 t \right )}}{2} - \frac {\cos {\left (2 t \right )}}{2} \]