83.5.11 problem 11

Internal problem ID [19027]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 11
Date solved : Thursday, March 13, 2025 at 01:24:30 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y \left (x \right ) = x^{2} \left (1+{\mathrm e}^{\frac {1}{x}} c_{1} \right ) \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.269 (sec). Leaf size: 14

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

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