Internal problem ID [12679]
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 1.8 page 121
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+3 y=\cos \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(y(t),t)+3*y(t)=cos(2*t),y(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \sin \left (2 t \right )}{13}+\frac {3 \cos \left (2 t \right )}{13}-\frac {16 \,{\mathrm e}^{-3 t}}{13} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 30
DSolve[{y'[t]+3*y[t]==Cos[2*t],{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{13} \left (2 \left (\sin (2 t)-8 e^{-3 t}\right )+3 \cos (2 t)\right ) \]