83.49.23 problem Ex 23 page 138

Internal problem ID [19557]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 23 page 138
Date solved : Thursday, March 13, 2025 at 02:49:29 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&=x^{3} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 28

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-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) - (-x**3/2 + x**2*Derivative(y(x), (x, 2))/2 + x*y(x) + y(x))/(x*(x + 1)) cannot be solved by the factorable group method