80.3.21 problem 22

Internal problem ID [21185]
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 : 22
Date solved : Thursday, October 02, 2025 at 07:16:09 PM
CAS classification : [_exact, _rational]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.500 (sec). Leaf size: 365

ode:=3*x^2-y(x)+(4*y(x)^3-x)*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\sqrt {6}\, \left (\sqrt {\frac {48 x^{3}+\left (108 x^{2}+12 \sqrt {-768 x^{9}+2304 x^{6}+81 x^{4}-2304 x^{3}+768}\right )^{{2}/{3}}-48}{\left (108 x^{2}+12 \sqrt {-768 x^{9}+2304 x^{6}+81 x^{4}-2304 x^{3}+768}\right )^{{1}/{3}}}}+\sqrt {-\frac {48 \left (\left (x^{3}+\frac {\left (108 x^{2}+12 \sqrt {-768 x^{9}+2304 x^{6}+81 x^{4}-2304 x^{3}+768}\right )^{{2}/{3}}}{48}-1\right ) \sqrt {\frac {48 x^{3}+\left (108 x^{2}+12 \sqrt {-768 x^{9}+2304 x^{6}+81 x^{4}-2304 x^{3}+768}\right )^{{2}/{3}}-48}{\left (108 x^{2}+12 \sqrt {-768 x^{9}+2304 x^{6}+81 x^{4}-2304 x^{3}+768}\right )^{{1}/{3}}}}-\frac {x \sqrt {6}\, \left (108 x^{2}+12 \sqrt {-768 x^{9}+2304 x^{6}+81 x^{4}-2304 x^{3}+768}\right )^{{1}/{3}}}{4}\right )}{\sqrt {\frac {48 x^{3}+\left (108 x^{2}+12 \sqrt {-768 x^{9}+2304 x^{6}+81 x^{4}-2304 x^{3}+768}\right )^{{2}/{3}}-48}{\left (108 x^{2}+12 \sqrt {-768 x^{9}+2304 x^{6}+81 x^{4}-2304 x^{3}+768}\right )^{{1}/{3}}}}\, \left (108 x^{2}+12 \sqrt {-768 x^{9}+2304 x^{6}+81 x^{4}-2304 x^{3}+768}\right )^{{1}/{3}}}}\right )}{12} \]

✗ Mathematica

ode=(3*x^2-y[x])+(4*y[x]^3-x)*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2 + (-x + 4*y(x)**3)*Derivative(y(x), x) - y(x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out