76.2.30 problem 30

Internal problem ID [17366]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 10:03:12 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=1+3 \sin \left (t \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=y_{0} \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 22

dsolve([diff(y(t),t)-y(t)=1+3*sin(t),y(0) = y__0],y(t), singsol=all)
 

\[ y = -1-\frac {3 \cos \left (t \right )}{2}-\frac {3 \sin \left (t \right )}{2}+{\mathrm e}^{t} y_{0} +\frac {5 \,{\mathrm e}^{t}}{2} \]

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 32

DSolve[{D[y[t],t]-y[t]==1+3*Sin[t],{y[0]==y0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t \left (\int _0^te^{-K[1]} (3 \sin (K[1])+1)dK[1]+\text {y0}\right ) \]