Internal problem ID [14085]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 48.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y=\sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve([diff(y(t),t)+y(t)=sin(t),y(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\cos \left (t \right )}{2}+\frac {\sin \left (t \right )}{2}-\frac {{\mathrm e}^{-t}}{2} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 23
DSolve[{y'[t]+y[t]==Sin[t],{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} \left (-e^{-t}+\sin (t)-\cos (t)\right ) \]