40.4.4 problem 19 (e)

Internal problem ID [6644]
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 : Monday, January 27, 2025 at 02:16:38 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 28

DSolve[D[i[t],t]-6*i[t]==10*Sin[2*t],i[t],t,IncludeSingularSolutions -> True]
 

\[ i(t)\to -\frac {1}{2} \cos (2 t)+c_1 e^{6 t}-3 \sin (t) \cos (t) \]