72.6.4 problem 4

Internal problem ID [14729]
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 : 4
Date solved : Tuesday, January 28, 2025 at 07:12:58 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(y(t),t)=2*y(t)+sin(2*t),y(t), singsol=all)
 

\[ y = -\frac {\cos \left (2 t \right )}{4}-\frac {\sin \left (2 t \right )}{4}+c_{1} {\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 33

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

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