23.3.129 problem 131

Internal problem ID [5843]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 131
Date solved : Tuesday, September 30, 2025 at 02:04:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 58

ode:=-x^3*y(x)+x^4*diff(y(x),x)+diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {9 \,{\mathrm e}^{-\frac {x^{5}}{5}} 5^{{3}/{5}} c_2 \left (x^{5}\right )^{{2}/{5}} \left (x^{5}+4\right )+25 c_1 \,x^{3}+25 \,{\mathrm e}^{-\frac {x^{5}}{10}} c_2 \,x^{5} \operatorname {WhittakerM}\left (\frac {2}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right )}{25 x^{2}} \]

✓ Mathematica. Time used: 0.097 (sec). Leaf size: 39

ode=-(x^3*y[x]) + x^4*D[y[x],x] + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x-\frac {c_2 \sqrt [5]{x^5} \Gamma \left (-\frac {1}{5},\frac {x^5}{5}\right )}{5 \sqrt [5]{5}} \end{align*}

✗ Sympy

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

False