71.4.16 problem 16

Internal problem ID [14317]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 16
Date solved : Monday, March 31, 2025 at 12:17:25 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=x^{2}+{\mathrm e}^{x}-\sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=-1 \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 23

ode:=diff(y(x),x) = x^2+exp(x)-sin(x); 
ic:=y(2) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {x^{3}}{3}+\cos \left (x \right )+{\mathrm e}^{x}-\frac {11}{3}-\cos \left (2\right )-{\mathrm e}^{2} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 28

ode=D[y[x],x]==x^2+Exp[x]-Sin[x]; 
ic={y[2]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _2^x\left (K[1]^2+e^{K[1]}-\sin (K[1])\right )dK[1]-1 \]

✓ Sympy. Time used: 0.184 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 - exp(x) + sin(x) + Derivative(y(x), x),0) 
ics = {y(2): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{3}}{3} + e^{x} + \cos {\left (x \right )} - e^{2} - \frac {11}{3} - \cos {\left (2 \right )} \]