83.40.7 problem 7

Internal problem ID [19408]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (E) at page 140
Problem number : 7
Date solved : Monday, March 31, 2025 at 07:12:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y&=-4 x^{3} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 17

ode:=x^2*diff(diff(y(x),x),x)-2*x*(1+x)*diff(y(x),x)+2*(1+x)*y(x) = -4*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left ({\mathrm e}^{2 x} c_1 +c_2 +2 x \right ) \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{2} x \left (4 x+c_2 e^{2 x}+2+2 c_1\right ) \]

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (2*x**3 + x**2*Derivative(y(x), (x, 2))/2 + x*y(x) + y(x))/(x*(x + 1)) cannot be solved by the factorable group method