Internal problem ID [5317]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {L i^{\prime }+R i=E \sin \left (2 t \right )} \] With initial conditions \begin {align*} [i \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 43
dsolve([L*diff(i(t),t)+R*i(t)=E*sin(2*t),i(0) = 0],i(t), singsol=all)
\[ i \left (t \right ) = -\frac {2 E \left (L \cos \left (2 t \right )-L \,{\mathrm e}^{-\frac {R t}{L}}-\frac {\sin \left (2 t \right ) R}{2}\right )}{4 L^{2}+R^{2}} \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 49
DSolve[{L*i'[t]+R*i[t]==e*Sin[2*t],{i[0]==0}},i[t],t,IncludeSingularSolutions -> True]
\[ i(t)\to \frac {2 e \left (L \left (e^{-\frac {R t}{L}}+\sin ^2(t)\right )-L \cos ^2(t)+R \sin (t) \cos (t)\right )}{4 L^2+R^2} \]