23.5.78 problem 78

Internal problem ID [6687]
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 : 78
Date solved : Tuesday, September 30, 2025 at 03:50:51 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} -2 y^{\prime }-\left (4+x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 40

ode:=-2*diff(y(x),x)-(4+x)*diff(diff(y(x),x),x)+(1-2*x)*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (c_3 -\int \frac {\left (2 c_1 x +c_2 \right ) {\mathrm e}^{\frac {x}{2}}}{\left (-1+2 x \right )^{{3}/{4}}}d x \right ) {\mathrm e}^{-\frac {x}{2}}}{\left (-1+2 x \right )^{{1}/{4}}} \]

✓ Mathematica. Time used: 60.453 (sec). Leaf size: 66

ode=-2*D[y[x],x] - (4 + x)*D[y[x],{x,2}] + (1 - 2*x)*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^xe^{-\frac {K[1]}{2}} \left (\frac {2 \sqrt {2} c_1 K[1]}{(2 K[1]-1)^{5/4}}+c_2 L_{-\frac {1}{4}}^{\frac {5}{4}}\left (\frac {K[1]}{2}-\frac {1}{4}\right )\right )dK[1]+c_3 \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE x*Derivative(y(x), (x, 2))/2 + x*Derivative(y(x), (x, 3)) + Deri