Internal problem ID [14093]
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: 56.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=-\cos \left (2 t \right )+\sin \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(t),t)=sin(2*t)-cos(2*t),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\sin \left (2 t \right )}{2}-\frac {\cos \left (2 t \right )}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 23
DSolve[{y'[t]==Sin[2*t]-Cos[2*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} (-\sin (2 t)-\cos (2 t)+1) \]