23.5.97 problem 97

Internal problem ID [6706]
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 : 97
Date solved : Tuesday, September 30, 2025 at 03:51:00 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x \left (x^{2}+3\right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 32

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

\[ y = \frac {\left (-12-6 \ln \left (x \right )^{2}+4 \left (-3+c_3 \right ) \ln \left (x \right )+x^{2}+4 c_2 x +4 c_1 \right ) x}{4} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to \frac {1}{4} x \left (x^2-6 \log ^2(x)+4 c_3 x+4 (-3+c_2) \log (x)+4 (-3+c_1)\right ) \end{align*}

✓ Sympy. Time used: 0.207 (sec). Leaf size: 26

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)) - x*(x**2 + 3) + 2*x*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x \left (C_{1} + C_{2} x + C_{3} \log {\left (x \right )} + x^{2} - 6 \log {\left (x \right )}^{2}\right )}{4} \]