88.12.12 problem 14

Internal problem ID [24068]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:56:53 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 )&=0 \\ y^{\prime }\left (0\right )&=1 \\ y^{\prime \prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 10

ode:=diff(diff(diff(y(x),x),x),x)+4*diff(y(x),x) = 0; 
ic:=[y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\sin \left (2 x \right )}{2} \]

✓ Mathematica. Time used: 0.116 (sec). Leaf size: 10

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

\begin{align*} y(x)&\to \sin (x) \cos (x) \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 8

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): 0, Subs(Derivative(y(x), x), x, 0): 1, Subs(Derivative(y(x), (x, 2)), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sin {\left (2 x \right )}}{2} \]