78.1.43 problem 4 (e)

Internal problem ID [18098]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 4 (e)
Date solved : Tuesday, January 28, 2025 at 11:26:17 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&={\mathrm e}^{x} \cos \left (x \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 15

dsolve([diff(y(x),x)=exp(x)*cos(x),y(0) = 0],y(x), singsol=all)
 

\[ y = -\frac {1}{2}+\frac {\left (\cos \left (x \right )+\sin \left (x \right )\right ) {\mathrm e}^{x}}{2} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 23

DSolve[{D[y[x],x]==Exp[x]*Cos[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (e^x \sin (x)+e^x \cos (x)-1\right ) \]