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 : Sunday, March 30, 2025 at 02:18:11 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*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 17

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

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

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

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

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

✓ Sympy. Time used: 0.146 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x)*sin(x) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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