82.39.11 problem Ex. 11

Internal problem ID [18872]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. End of chapter problems at page 91
Problem number : Ex. 11
Date solved : Monday, March 31, 2025 at 06:17:41 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 30

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

\[ y = \frac {4 c_3 \,x^{2} \ln \left (x \right )+4 c_1 \,x^{2}+\ln \left (x \right )+4 c_2 +1}{4 x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 33

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

\[ y(x)\to \frac {\log (x)+1}{4 x}+\frac {c_1}{x}+c_2 x+c_3 x \log (x) \]

✓ Sympy. Time used: 0.357 (sec). Leaf size: 22

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

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