23.5.30 problem 30

Internal problem ID [6639]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 30
Date solved : Tuesday, September 30, 2025 at 03:50:26 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.094 (sec). Leaf size: 1140

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

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

✓ Mathematica. Time used: 0.145 (sec). Leaf size: 4693

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

Too large to display

✓ Sympy. Time used: 0.334 (sec). Leaf size: 182

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (-2 - \frac {5}{\sqrt [3]{46 + 3 \sqrt {249}}} + \sqrt [3]{46 + 3 \sqrt {249}}\right )}{6}} \sin {\left (\frac {\sqrt {3} x \left (\frac {5}{\sqrt [3]{46 + 3 \sqrt {249}}} + \sqrt [3]{46 + 3 \sqrt {249}}\right )}{6} \right )} + C_{2} e^{\frac {x \left (-2 - \frac {5}{\sqrt [3]{46 + 3 \sqrt {249}}} + \sqrt [3]{46 + 3 \sqrt {249}}\right )}{6}} \cos {\left (\frac {\sqrt {3} x \left (\frac {5}{\sqrt [3]{46 + 3 \sqrt {249}}} + \sqrt [3]{46 + 3 \sqrt {249}}\right )}{6} \right )} + C_{3} e^{\frac {x \left (- \sqrt [3]{46 + 3 \sqrt {249}} - 1 + \frac {5}{\sqrt [3]{46 + 3 \sqrt {249}}}\right )}{3}} + \frac {\cos {\left (2 x \right )}}{4} \]