23.1.16 problem 2(f)

Internal problem ID [4106]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(f)
Date solved : Monday, January 27, 2025 at 08:08:59 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 24

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

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