23.3.264 problem 266

Internal problem ID [5978]
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 : 266
Date solved : Tuesday, September 30, 2025 at 02:07:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to \frac {1}{4} x \left (x^2+12 x+4 c_2 \log (x)+4 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {x \left (C_{1} + C_{2} \log {\left (x \right )} + x^{2} + 12 x\right )}{4} \]