23.5.98 problem 98

Internal problem ID [6707]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 98
Date solved : Tuesday, September 30, 2025 at 03:51:01 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} -8 y+3 x y^{\prime }+x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=-8*y(x)+3*x*diff(y(x),x)+x^2*diff(diff(y(x),x),x)+x^3*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 28

ode=-8*y[x] + 3*x*D[y[x],x] + x^2*D[y[x],{x,2}] + x^3*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.131 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + x**2*Derivative(y(x), (x, 2)) + 3*x*Derivative(y(x), x) - 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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