15.15.4 problem 4

Internal problem ID [3208]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 4
Date solved : Sunday, March 30, 2025 at 01:21:15 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(diff(y(x),x),x),x)+4*diff(y(x),x) = exp(x)+sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sin \left (2 x \right ) c_1}{2}-\frac {\cos \left (2 x \right ) c_2}{2}+\frac {{\mathrm e}^{x}}{5}-\frac {\cos \left (x \right )}{3}+c_3 \]

✓ Mathematica. Time used: 0.228 (sec). Leaf size: 37

ode=D[y[x],{x,3}]+4*D[y[x],x]==Exp[x]+Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^x}{5}-\frac {1}{2} c_2 \cos (2 x)+\cos (x) \left (-\frac {1}{3}+c_1 \sin (x)\right )+c_3 \]

✓ Sympy. Time used: 0.210 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x) - sin(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} \sin {\left (2 x \right )} + C_{3} \cos {\left (2 x \right )} + \frac {e^{x}}{5} - \frac {\cos {\left (x \right )}}{3} \]