72.6.16 problem 24

Internal problem ID [14741]
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
Date solved : Tuesday, January 28, 2025 at 07:13:21 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t)+y(t)=cos(2*t)+3*sin(2*t)+exp(-t),y(t), singsol=all)
 

\[ y = \left (t +c_{1} \right ) {\mathrm e}^{-t}-\cos \left (2 t \right )+\sin \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 44

DSolve[D[y[t],t]+y[t]==Cos[2*t]+3*Sin[2*t]+Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (\int _1^t\left (e^{K[1]} \cos (2 K[1])+3 e^{K[1]} \sin (2 K[1])+1\right )dK[1]+c_1\right ) \]