23.3.282 problem 284

Internal problem ID [5996]
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 : 284
Date solved : Tuesday, September 30, 2025 at 02:07:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y-2 x y^{\prime }+x^{2} y^{\prime \prime }&=4 x^{3} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=2*y(x)-2*x*diff(y(x),x)+x^2*diff(diff(y(x),x),x) = 4*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{2}+2 x^{3}+c_2 x \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.190 (sec). Leaf size: 14

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

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