15.16.15 problem 15

Internal problem ID [3235]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 15
Date solved : Sunday, March 30, 2025 at 01:23:27 AM
CAS classification : [[_high_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y&=\cos \left (\ln \left (x \right )\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 49

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)+7*x^3*diff(diff(diff(y(x),x),x),x)+9*x^2*diff(diff(y(x),x),x)-6*x*diff(y(x),x)-6*y(x) = cos(ln(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1320 \cos \left (\sqrt {2}\, \ln \left (x \right )\right ) c_3 +1320 \sin \left (\sqrt {2}\, \ln \left (x \right )\right ) c_4 +\left (-33-66 i\right ) x^{1-i}+\left (-33+66 i\right ) x^{1+i}+120 c_2 \,x^{3}-220 c_1}{1320 x} \]

✓ Mathematica. Time used: 0.345 (sec). Leaf size: 62

ode=x^4*D[y[x],{x,4}]+7*x^3*D[y[x],{x,3}]+9*x^2*D[y[x],{x,2}]-6*x*D[y[x],x]-6*y[x]==Cos[Log[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_4 x^2+\frac {c_3}{x}-\frac {1}{10} \sin (\log (x))-\frac {1}{20} \cos (\log (x))+\frac {c_2 \cos \left (\sqrt {2} \log (x)\right )}{x}+\frac {c_1 \sin \left (\sqrt {2} \log (x)\right )}{x} \]

✓ Sympy. Time used: 0.702 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) + 7*x**3*Derivative(y(x), (x, 3)) + 9*x**2*Derivative(y(x), (x, 2)) - 6*x*Derivative(y(x), x) - 6*y(x) - cos(log(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + C_{3} \sin {\left (\sqrt {2} \log {\left (x \right )} \right )} + C_{4} \cos {\left (\sqrt {2} \log {\left (x \right )} \right )} + \frac {x \left (C_{2} x^{2} - 2 \sin {\left (\log {\left (x \right )} \right )} - \cos {\left (\log {\left (x \right )} \right )}\right )}{20}}{x} \]