72.7.21 problem 21

Internal problem ID [14762]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 07:14:27 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} v^{\prime }+\frac {2 v}{5}&=3 \cos \left (2 t \right ) \end{align*}

✓ Solution by Maple

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

dsolve(diff(v(t),t)+4/10*v(t)=3*cos(2*t),v(t), singsol=all)
 

\[ v = \frac {15 \cos \left (2 t \right )}{52}+\frac {75 \sin \left (2 t \right )}{52}+{\mathrm e}^{-\frac {2 t}{5}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.096 (sec). Leaf size: 38

DSolve[D[ v[t],t]+4/10*v[t]==3*Cos[2*t],v[t],t,IncludeSingularSolutions -> True]
 

\[ v(t)\to e^{-2 t/5} \left (\int _1^t3 e^{\frac {2 K[1]}{5}} \cos (2 K[1])dK[1]+c_1\right ) \]