76.39.6 problem Ex. 6

Internal problem ID [20223]
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. 6
Date solved : Thursday, October 02, 2025 at 05:34:54 PM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 c +\frac {10}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 38

ode:=x^3*diff(diff(diff(y(x),x),x),x)+2*x^2*diff(diff(y(x),x),x)+2*y(x) = 10*c+10/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {5 x^{2} \sin \left (\ln \left (x \right )\right ) c_3 +5 x^{2} \cos \left (\ln \left (x \right )\right ) c_2 +25 c x +10 \ln \left (x \right )+c_1 +8}{5 x} \]

✓ Mathematica. Time used: 0.078 (sec). Leaf size: 43

ode=x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]+2*y[x]==10*(c+1/x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 5 c+\frac {8}{5 x}+\frac {2 \log (x)}{x}+\frac {c_3}{x}+c_2 x \cos (\log (x))+c_1 x \sin (\log (x)) \end{align*}

✓ Sympy. Time used: 0.287 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
c = symbols("c") 
y = Function("y") 
ode = Eq(-10*c + x**3*Derivative(y(x), (x, 3)) + 2*x**2*Derivative(y(x), (x, 2)) + 2*y(x) - 10/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + x \left (C_{2} x \sin {\left (\log {\left (x \right )} \right )} + C_{3} x \cos {\left (\log {\left (x \right )} \right )} + 5 c\right ) + 2 \log {\left (x \right )}}{x} \]