83.27.12 problem 12

Internal problem ID [19287]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (A) at page 104
Problem number : 12
Date solved : Monday, March 31, 2025 at 07:05:43 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=(-b*x^2+a*x)*diff(diff(y(x),x),x)+2*a*diff(y(x),x)+2*b*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 +\left (-b x +a \right )^{3} c_2}{x} \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 32

ode=(a*x-b*x^2)*D[y[x],{x,2}]+2*a*D[y[x],x]+2*b*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\frac {c_2 (b x-a)^3}{b}+3 c_1}{3 x} \]

✗ Sympy

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

False