67.12.13 problem 19.3 (a)

Internal problem ID [16652]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.3 (a)
Date solved : Thursday, October 02, 2025 at 01:37:22 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ y^{\prime }\left (0\right )&=6 \\ y^{\prime \prime }\left (0\right )&=8 \\ \end{align*}

✓ Maple. Time used: 0.055 (sec). Leaf size: 18

ode:=diff(diff(diff(y(x),x),x),x)+4*diff(y(x),x) = 0; 
ic:=[y(0) = 4, D(y)(0) = 6, (D@@2)(y)(0) = 8]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 6+3 \sin \left (2 x \right )-2 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 51.567 (sec). Leaf size: 53

ode=D[y[x],{x,3}]+4*D[y[x],x]==0; 
ic={y[0]==4,Derivative[1][y][0] ==6,Derivative[2][y][0] ==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x(6 \cos (2 K[1])+4 \sin (2 K[1]))dK[1]-\int _1^0(6 \cos (2 K[1])+4 \sin (2 K[1]))dK[1]+4 \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 4, Subs(Derivative(y(x), x), x, 0): 6, Subs(Derivative(y(x), (x, 2)), x, 0): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 \sin {\left (2 x \right )} - 2 \cos {\left (2 x \right )} + 6 \]