83.4.8 problem 8

Internal problem ID [19009]
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 (C) at page 12
Problem number : 8
Date solved : Monday, March 31, 2025 at 06:31:51 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (2 x -2 y+5\right ) y^{\prime }-x +y-3&=0 \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 19

ode:=(2*x-2*y(x)+5)*diff(y(x),x)-x+y(x)-3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{x +4-c_1}\right )}{2}+x +2 \]

✓ Mathematica. Time used: 3.153 (sec). Leaf size: 29

ode=(2*x-2*y[x]+5)*D[y[x],x]-(x-y[x]+3)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {1}{2} W\left (-e^{x-1+c_1}\right )+x+2 \\ y(x)\to x+2 \\ \end{align*}

✓ Sympy. Time used: 0.968 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (2*x - 2*y(x) + 5)*Derivative(y(x), x) + y(x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x - \frac {W\left (C_{1} e^{x + 4}\right )}{2} + 2 \]