82.39.1 problem Ex. 1

Internal problem ID [18862]
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. 1
Date solved : Monday, March 31, 2025 at 06:17:23 PM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=diff(diff(diff(y(x),x),x),x)-4/x*diff(diff(y(x),x),x)+5/x^2*diff(y(x),x)-2/x^3*y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{\frac {5}{2}+\frac {\sqrt {21}}{2}} c_3 +x^{\frac {5}{2}-\frac {\sqrt {21}}{2}} c_2 -\frac {x^{2} \left (c_1 +x \right )}{5} \]

✓ Mathematica. Time used: 0.07 (sec). Leaf size: 53

ode=D[y[x],{x,3}]-4/x*D[y[x],{x,2}]+5/x^2*D[y[x],x]-2/x^3*y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 x^{\frac {1}{2} \left (5+\sqrt {21}\right )}+c_1 x^{\frac {5}{2}-\frac {\sqrt {21}}{2}}-\frac {x^3}{5}+c_3 x^2 \]

✓ Sympy. Time used: 0.424 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 3)) - 1 - 4*Derivative(y(x), (x, 2))/x + 5*Derivative(y(x), x)/x**2 - 2*y(x)/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{2} + C_{2} x^{\frac {5}{2} - \frac {\sqrt {21}}{2}} + C_{3} x^{\frac {\sqrt {21}}{2} + \frac {5}{2}} - \frac {x^{3}}{5} \]