83.23.32 problem 31 (b)

Internal problem ID [19242]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 31 (b)
Date solved : Monday, March 31, 2025 at 07:02:44 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {c_1 x +b}{b x +1} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 24

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

\begin{align*} y(x)\to \frac {b+c_1 x}{b x+1} \\ y(x)\to b \\ \end{align*}

✓ Sympy. Time used: 0.325 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {C_{1} x}{x + \frac {1}{b}} + b \]