77.14.4 problem 4

Internal problem ID [20468]
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. Exercise III (F) at page 42
Problem number : 4
Date solved : Thursday, October 02, 2025 at 06:03:10 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-12 y&=\cos \left (4 x \right ) \end{align*}

✓ Maple. Time used: 0.101 (sec). Leaf size: 1264

ode:=diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-diff(y(x),x)-12*y(x) = cos(4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 0.223 (sec). Leaf size: 4269

ode=D[y[x],{x,3}]+3*D[y[x],{x,2}]-D[y[x],{x,2}]-12*y[x]==Cos[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✓ Sympy. Time used: 0.437 (sec). Leaf size: 241

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*y(x) - cos(4*x) - Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x \left (\frac {2 \sqrt [3]{18}}{3 \sqrt [3]{\sqrt {5793} + 81}} + 1 + \frac {\sqrt [3]{12} \sqrt [3]{\sqrt {5793} + 81}}{12}\right )} \sin {\left (\sqrt [3]{2} \sqrt [6]{3} x \left (- \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} \sqrt [3]{\sqrt {5793} + 81}}{12} + \frac {2}{\sqrt [3]{\sqrt {5793} + 81}}\right ) \right )} + C_{2} e^{- x \left (\frac {2 \sqrt [3]{18}}{3 \sqrt [3]{\sqrt {5793} + 81}} + 1 + \frac {\sqrt [3]{12} \sqrt [3]{\sqrt {5793} + 81}}{12}\right )} \cos {\left (\sqrt [3]{2} \sqrt [6]{3} x \left (- \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} \sqrt [3]{\sqrt {5793} + 81}}{12} + \frac {2}{\sqrt [3]{\sqrt {5793} + 81}}\right ) \right )} + C_{3} e^{x \left (-1 + \frac {4 \sqrt [3]{18}}{3 \sqrt [3]{\sqrt {5793} + 81}} + \frac {\sqrt [3]{12} \sqrt [3]{\sqrt {5793} + 81}}{6}\right )} - \frac {17 \sin {\left (4 x \right )}}{2056} - \frac {15 \cos {\left (4 x \right )}}{2056} \]