15.14.30 problem 32

Internal problem ID [3202]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 32
Date solved : Sunday, March 30, 2025 at 01:21:06 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 38

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-2*diff(y(x),x) = exp(-2*x)*cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (104 c_1 \,{\mathrm e}^{3 x}+104 c_3 \,{\mathrm e}^{2 x}+\sin \left (2 x \right )+5 \cos \left (2 x \right )-52 c_2 \right ) {\mathrm e}^{-2 x}}{104} \]

✓ Mathematica. Time used: 0.813 (sec). Leaf size: 42

ode=D[y[x],{x,3}]+D[y[x],{x,2}]-2*D[y[x],x]==Exp[-2*x]*Cos[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{104} e^{-2 x} \left (\sin (2 x)+5 \cos (2 x)-52 \left (c_1-2 c_2 e^{3 x}\right )\right )+c_3 \]

✓ Sympy. Time used: 0.390 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = C_{1} + C_{3} e^{x} + \left (C_{2} + \frac {\sin {\left (2 x \right )}}{104} + \frac {5 \cos {\left (2 x \right )}}{104}\right ) e^{- 2 x} \]