74.1.49 problem 56

Internal problem ID [15829]
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
Date solved : Tuesday, January 28, 2025 at 08:08:26 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 18

dsolve([diff(y(t),t)=sin(2*t)-cos(2*t),y(0) = 0],y(t), singsol=all)
 

\[ y = -\frac {\sin \left (2 t \right )}{2}-\frac {\cos \left (2 t \right )}{2}+\frac {1}{2} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 25

DSolve[{D[y[t],t]==Sin[2*t]-Cos[2*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _0^t(\sin (2 K[1])-\cos (2 K[1]))dK[1] \]