37.2.6 problem 10.3.7

Internal problem ID [6403]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.3, ODEs with variable Coefficients. First order. page 315
Problem number : 10.3.7
Date solved : Wednesday, March 05, 2025 at 12:39:11 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{1-x}+x -x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(y(x),x)+y(x)/(1-x)+x-x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (x^{2}+2 c_1 \right ) \left (x -1\right )}{2} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 20

ode=D[y[x],x]+y[x]/(1-x)+x-x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.270 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} x - C_{1} + \frac {x^{3}}{2} - \frac {x^{2}}{2} \]