80.3.17 problem 18

Internal problem ID [21181]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 18
Date solved : Thursday, October 02, 2025 at 07:15:56 PM
CAS classification : [_separable]

\begin{align*} 2 x^{2}+1&=\left (y^{5}-1\right ) y^{\prime } \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=2*x^2+1 = (y(x)^5-1)*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {2 x^{3}}{3}+x -\frac {y^{6}}{6}+y+c_1 = 0 \]

✓ Mathematica. Time used: 5.23 (sec). Leaf size: 169

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

\begin{align*} y(x)&\to \text {Root}\left [\text {$\#$1}^6-6 \text {$\#$1}-4 x^3-6 x-6 c_1\&,1\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^6-6 \text {$\#$1}-4 x^3-6 x-6 c_1\&,2\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^6-6 \text {$\#$1}-4 x^3-6 x-6 c_1\&,3\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^6-6 \text {$\#$1}-4 x^3-6 x-6 c_1\&,4\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^6-6 \text {$\#$1}-4 x^3-6 x-6 c_1\&,5\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^6-6 \text {$\#$1}-4 x^3-6 x-6 c_1\&,6\right ] \end{align*}

✓ Sympy. Time used: 0.119 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2 - (y(x)**5 - 1)*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - \frac {2 x^{3}}{3} - x + \frac {y^{6}{\left (x \right )}}{6} - y{\left (x \right )} = C_{1} \]