83.40.8 problem 8

Internal problem ID [19409]
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 : 8
Date solved : Monday, March 31, 2025 at 07:12:52 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 18

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

\[ y = c_2 x +{\mathrm e}^{x} c_1 -x^{2}-1 \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 25

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

\[ y(x)\to -x^2-(1+c_2) x+c_1 e^x-1 \]

✗ Sympy

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

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