85.1.15 problem 11 (a)

Internal problem ID [22420]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 11 (a)
Date solved : Thursday, October 02, 2025 at 08:39:09 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 \sin \left (x \right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 10

ode:=diff(y(x),x) = 3*sin(x); 
ic:=[y(Pi) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -3 \cos \left (x \right )-4 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 11

ode=D[y[x],{x,1}]==3*Sin[x]; 
ic={y[Pi]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -3 \cos (x)-4 \end{align*}

✓ Sympy. Time used: 0.067 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*sin(x) + Derivative(y(x), x),0) 
ics = {y(pi): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 3 \cos {\left (x \right )} - 4 \]