85.64.13 problem 3 (b)

Internal problem ID [22880]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 213
Problem number : 3 (b)
Date solved : Thursday, October 02, 2025 at 09:16:09 PM
CAS classification : [[_high_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+x y^{\prime }-y&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^3*diff(diff(diff(y(x),x),x),x)+7*x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {c_1 +4 x}{4 x}+c_2 x +c_3 \cos \left (\ln \left (x \right )\right )+c_4 \sin \left (\ln \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 29

ode=x^4*D[y[x],{x,4}]+6*x^3*D[y[x],{x,3}]+7*x^2*D[y[x],{x,2}]+x*D[y[x],{x,1}]-y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x+\frac {c_3}{x}+c_2 \cos (\log (x))+c_4 \sin (\log (x))-1 \end{align*}

✓ Sympy. Time used: 0.303 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) + 6*x**3*Derivative(y(x), (x, 3)) + 7*x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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