Internal problem ID [12678]
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: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y=\cos \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(y(t),t)+y(t)=cos(2*t),y(0) = 5],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \sin \left (2 t \right )}{5}+\frac {\cos \left (2 t \right )}{5}+\frac {24 \,{\mathrm e}^{-t}}{5} \]
✓ Solution by Mathematica
Time used: 0.144 (sec). Leaf size: 27
DSolve[{y'[t]+y[t]==Cos[2*t],{y[0]==5}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{5} \left (24 e^{-t}+2 \sin (2 t)+\cos (2 t)\right ) \]