40.4.20 problem 22 (b)

Internal problem ID [6660]
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 : 22 (b)
Date solved : Monday, January 27, 2025 at 02:18:21 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} L i^{\prime }+R i&=E \sin \left (2 t \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 43

dsolve([L*diff(i(t),t)+R*i(t)=E*sin(2*t),i(0) = 0],i(t), singsol=all)
 

\[ i = -\frac {2 E \left (L \cos \left (2 t \right )-L \,{\mathrm e}^{-\frac {R t}{L}}-\frac {\sin \left (2 t \right ) R}{2}\right )}{4 L^{2}+R^{2}} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 49

DSolve[{L*D[i[t],t]+R*i[t]==e*Sin[2*t],{i[0]==0}},i[t],t,IncludeSingularSolutions -> True]
 

\[ i(t)\to \frac {2 e \left (L \left (e^{-\frac {R t}{L}}+\sin ^2(t)\right )-L \cos ^2(t)+R \sin (t) \cos (t)\right )}{4 L^2+R^2} \]