89.10.31 problem 32

Internal problem ID [24524]
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 : 32
Date solved : Thursday, October 02, 2025 at 10:45:34 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x -y-1-2 \left (-2+y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.198 (sec). Leaf size: 214

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

\[ y = \frac {-2 c_1 \left (x -7\right ) \left (x -3\right )^{2} {\left (\sqrt {-\left (-1+\left (x -3\right )^{3} c_1 \right ) c_1^{2} \left (x -3\right )^{6}}+\left (x^{3}-9 x^{2}+27 x -27\right ) c_1 \right )}^{{2}/{3}}+i \left (-\left (x -3\right )^{6} c_1^{2}+\left (c_1 \,x^{3}-9 c_1 \,x^{2}+27 c_1 x +\sqrt {-\left (-1+\left (x -3\right )^{3} c_1 \right ) c_1^{2} \left (x -3\right )^{6}}-27 c_1 \right )^{{4}/{3}}\right ) \sqrt {3}+\left (x -3\right )^{6} c_1^{2}+\left (c_1 \,x^{3}-9 c_1 \,x^{2}+27 c_1 x +\sqrt {-\left (-1+\left (x -3\right )^{3} c_1 \right ) c_1^{2} \left (x -3\right )^{6}}-27 c_1 \right )^{{4}/{3}}}{4 {\left (\sqrt {-\left (-1+\left (x -3\right )^{3} c_1 \right ) c_1^{2} \left (x -3\right )^{6}}+\left (x^{3}-9 x^{2}+27 x -27\right ) c_1 \right )}^{{2}/{3}} c_1 \left (x -3\right )^{2}} \]

✓ Mathematica. Time used: 60.043 (sec). Leaf size: 757

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 150.230 (sec). Leaf size: 729

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x - (2*y(x) - 4)*Derivative(y(x), x) - y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]