15.12.9 problem 9

Internal problem ID [3153]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 9
Date solved : Sunday, March 30, 2025 at 01:19:50 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }&=\cos \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

ode:=diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-4*diff(y(x),x) = cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_2 -\frac {{\mathrm e}^{-4 x} c_1}{4}-\frac {\sin \left (2 x \right )}{25}-\frac {3 \cos \left (2 x \right )}{100}+c_3 \]

✓ Mathematica. Time used: 0.333 (sec). Leaf size: 41

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

\[ y(x)\to -\frac {1}{25} \sin (2 x)-\frac {3}{100} \cos (2 x)-\frac {1}{4} c_1 e^{-4 x}+c_2 e^x+c_3 \]

✓ Sympy. Time used: 0.245 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 4 x} + C_{3} e^{x} - \frac {\sin {\left (2 x \right )}}{25} - \frac {3 \cos {\left (2 x \right )}}{100} \]