83.48.21 problem Ex 22 page 117

Internal problem ID [19542]
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 VII. Exact differential equations.
Problem number : Ex 22 page 117
Date solved : Monday, March 31, 2025 at 07:32:49 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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