Internal problem ID [14282]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 60 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+\frac {y}{2}=\sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = a] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([diff(y(t),t)+y(t)/2=sin(t),y(0) = a],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-\frac {t}{2}} a +\frac {2 \sin \left (t \right )}{5}+\frac {4 \,{\mathrm e}^{-\frac {t}{2}}}{5}-\frac {4 \cos \left (t \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 37
DSolve[{y'[t]+y[t]/2==Sin[t],{y[0]==a}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{5} \left (5 a e^{-t/2}+4 e^{-t/2}+2 \sin (t)-4 \cos (t)\right ) \]