89.10.27 problem 28

Internal problem ID [24520]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 77
Problem number : 28
Date solved : Thursday, October 02, 2025 at 10:45:02 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +4 y+3-\left (2 x -y-3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 29

ode:=x+4*y(x)+3-(2*x-y(x)-3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-x \operatorname {LambertW}\left (3 c_1 \left (x -1\right )\right )-3 x +3}{\operatorname {LambertW}\left (3 c_1 \left (x -1\right )\right )} \]

✓ Mathematica. Time used: 2.897 (sec). Leaf size: 137

ode=( x+4*y[x]+3)-( 2*x-y[x]-3 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {2^{2/3} \left (x \log \left (\frac {1-x}{y(x)-2 x+3}\right )-x \log \left (\frac {y(x)+x}{y(x)-2 x+3}\right )+y(x) \left (\log \left (\frac {9\ 2^{2/3} (x-1)}{-y(x)+2 x-3}\right )-\log \left (-\frac {3\ 2^{2/3} (y(x)+x)}{-y(x)+2 x-3}\right )+1\right )-2 x+x \log (9)-x \log (3)+3\right )}{9 (y(x)+x)}=\frac {1}{9} 2^{2/3} \log (x-1)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.704 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x - (2*x - y(x) - 3)*Derivative(y(x), x) + 4*y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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