83.44.8 problem Ex 8 page 40

Internal problem ID [19457]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter III. Ordinary linear differential equations with constant coefficients
Problem number : Ex 8 page 40
Date solved : Thursday, March 13, 2025 at 02:31:50 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 48

ode:=diff(diff(diff(y(x),x),x),x)+a^2*diff(y(x),x) = sin(a*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\left (2 a^{2} c_{1} -a x \right ) \sin \left (a x \right )+2 c_3 \,a^{3}-2 \cos \left (a x \right ) c_{2} a^{2}-2 \cos \left (a x \right )}{2 a^{3}} \]

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 46

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

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

✓ Sympy. Time used: 0.253 (sec). Leaf size: 32

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

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