Internal problem ID [13005]
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: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y=\cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(t),t)+y(t)=cos(2*t)+3*sin(2*t)+exp(-t),y(t), singsol=all)
\[ y \left (t \right ) = \left (t +c_{1} \right ) {\mathrm e}^{-t}-\cos \left (2 t \right )+\sin \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.239 (sec). Leaf size: 32
DSolve[y'[t]+y[t]==Cos[2*t]+3*Sin[2*t]+Exp[-t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} \left (t+e^t \sin (2 t)-e^t \cos (2 t)+c_1\right ) \]