88.8.1 problem 1

Internal problem ID [24009]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 44
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:53:48 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 20 y-20 x y^{2}+\left (5 x -8 x^{2} y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 55

ode:=20*y(x)-20*x*y(x)^2+(5*x-8*x^2*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {5 x^{2}+\sqrt {25 x^{4}+16 c_1 x}}{8 x^{3}} \\ y &= \frac {5 x^{2}-\sqrt {25 x^{4}+16 c_1 x}}{8 x^{3}} \\ \end{align*}

✓ Mathematica. Time used: 0.52 (sec). Leaf size: 86

ode=( 20*y[x]-20*x*y[x]^2 )+( 5*x-8*x^2*y[x] )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {5 x^4-\sqrt {x^3} \sqrt {25 x^5+64 c_1 x^2}}{8 x^5}\\ y(x)&\to \frac {5 x^4+\sqrt {x^3} \sqrt {25 x^5+64 c_1 x^2}}{8 x^5} \end{align*}

✓ Sympy. Time used: 0.667 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-20*x*y(x)**2 + (-8*x**2*y(x) + 5*x)*Derivative(y(x), x) + 20*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {5 - \sqrt {\frac {C_{1}}{x^{3}} + 25}}{8 x}, \ y{\left (x \right )} = \frac {\sqrt {\frac {C_{1}}{x^{3}} + 25} + 5}{8 x}\right ] \]