85.27.3 problem 3

Internal problem ID [22595]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 60
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:54:49 PM
CAS classification : [[_3rd_order, _quadrature]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=0 \\ y^{\prime \prime }\left (0\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 15

ode:=diff(diff(diff(y(x),x),x),x) = 3*sin(x); 
ic:=[y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = -2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 18

ode=D[y[x],{x,3}]==3*Sin[x]; 
ic={y[0]==1,Derivative[1][y][0] ==0,Derivative[2][y][0] ==-2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \left (x^2+6 \cos (x)-4\right ) \end{align*}

✓ Sympy. Time used: 0.043 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*sin(x) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 0, Subs(Derivative(y(x), (x, 2)), x, 0): -2} 
dsolve(ode,func=y(x),ics=ics)
 

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