83.17.11 problem 11

Internal problem ID [19136]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Misc. Examples on chapter III at page 50
Problem number : 11
Date solved : Monday, March 31, 2025 at 06:49:29 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=96 \sin \left (2 x \right ) \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 41

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+10*diff(diff(y(x),x),x)+9*y(x) = 96*sin(2*x)*cos(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x +c_3 \right ) \cos \left (3 x \right )+\frac {\left (12 c_4 -11\right ) \sin \left (3 x \right )}{12}+\left (-3 x +c_1 \right ) \cos \left (x \right )+\frac {\sin \left (x \right ) \left (2 c_2 -3\right )}{2} \]

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 50

ode=D[y[x],{x,4}]+10*D[y[x],{x,2}]+9*y[x]==96*Sin[2*x]*Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {3 \sin (x)}{2}-\frac {7}{6} \sin (3 x)+(-3 x+c_3) \cos (x)+(x+c_1) \cos (3 x)+c_4 \sin (x)+c_2 \sin (3 x) \]

✓ Sympy. Time used: 1.902 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 96*sin(2*x)*cos(x) + 10*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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