Internal problem ID [13026]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {v^{\prime }+\frac {2 v}{5}=3 \cos \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(v(t),t)+4/10*v(t)=3*cos(2*t),v(t), singsol=all)
\[ v \left (t \right ) = \frac {15 \cos \left (2 t \right )}{52}+\frac {75 \sin \left (2 t \right )}{52}+{\mathrm e}^{-\frac {2 t}{5}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 31
DSolve[v'[t]+4/10*v[t]==3*Cos[2*t],v[t],t,IncludeSingularSolutions -> True]
\[ v(t)\to \frac {15}{52} (5 \sin (2 t)+\cos (2 t))+c_1 e^{-2 t/5} \]