15.14.28 problem 30

Internal problem ID [3200]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 30
Date solved : Tuesday, March 04, 2025 at 04:05:48 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.041 (sec). Leaf size: 1302

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(y(x),x),x)+diff(y(x),x) = x^3-1/2*cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 6.695 (sec). Leaf size: 1293

ode=D[y[x],{x,4}]+2*D[y[x],{x,2}]+D[y[x],x]==x^3-1/2*Cos[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 0.540 (sec). Leaf size: 264

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{\frac {\sqrt [3]{6} x \left (- \frac {4 \sqrt [3]{3}}{\sqrt [3]{9 + \sqrt {177}}} + \sqrt [3]{2} \sqrt [3]{9 + \sqrt {177}}\right )}{12}} \sin {\left (\sqrt [3]{2} \sqrt [6]{3} x \left (\frac {1}{\sqrt [3]{9 + \sqrt {177}}} + \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} \sqrt [3]{9 + \sqrt {177}}}{12}\right ) \right )} + C_{3} e^{\frac {\sqrt [3]{6} x \left (- \frac {4 \sqrt [3]{3}}{\sqrt [3]{9 + \sqrt {177}}} + \sqrt [3]{2} \sqrt [3]{9 + \sqrt {177}}\right )}{12}} \cos {\left (\sqrt [3]{2} \sqrt [6]{3} x \left (\frac {1}{\sqrt [3]{9 + \sqrt {177}}} + \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} \sqrt [3]{9 + \sqrt {177}}}{12}\right ) \right )} + C_{4} e^{- \frac {\sqrt [3]{6} x \left (- \frac {4 \sqrt [3]{3}}{\sqrt [3]{9 + \sqrt {177}}} + \sqrt [3]{2} \sqrt [3]{9 + \sqrt {177}}\right )}{6}} + \frac {x^{4}}{4} - 2 x^{3} + 12 x^{2} - 54 x - \frac {\sin {\left (2 x \right )}}{68} - \frac {\cos {\left (2 x \right )}}{17} \]