88.7.2 problem 2
Internal
problem
ID
[23997]
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
41
Problem
number
:
2
Date
solved
:
Thursday, October 02, 2025 at 09:50:26 PM
CAS
classification
:
[_exact, _rational]
\begin{align*} 3 x^{2} y^{2}-4 y+\left (3 y^{2}-4 x +2 x^{3} y\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 477
ode:=3*x^2*y(x)^2-4*y(x)+(3*y(x)^2-4*x+2*x^3*y(x))*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {\left (-144 x^{4}-108 c_1 -8 x^{9}+12 \sqrt {12 c_1 \,x^{9}-48 x^{8}+216 c_1 \,x^{4}-768 x^{3}+81 c_1^{2}}\right )^{{1}/{3}}}{6}+\frac {2 x \left (x^{5}+12\right )}{3 \left (-144 x^{4}-108 c_1 -8 x^{9}+12 \sqrt {12 c_1 \,x^{9}-48 x^{8}+216 c_1 \,x^{4}-768 x^{3}+81 c_1^{2}}\right )^{{1}/{3}}}-\frac {x^{3}}{3} \\
y &= \frac {\left (-i \sqrt {3}-1\right ) \left (-144 x^{4}-108 c_1 -8 x^{9}+12 \sqrt {12 c_1 \,x^{9}-48 x^{8}+216 c_1 \,x^{4}-768 x^{3}+81 c_1^{2}}\right )^{{1}/{3}}}{12}+\frac {x \left (-x^{2} \left (-144 x^{4}-108 c_1 -8 x^{9}+12 \sqrt {12 c_1 \,x^{9}-48 x^{8}+216 c_1 \,x^{4}-768 x^{3}+81 c_1^{2}}\right )^{{1}/{3}}+\left (i \sqrt {3}-1\right ) \left (x^{5}+12\right )\right )}{3 \left (-144 x^{4}-108 c_1 -8 x^{9}+12 \sqrt {12 c_1 \,x^{9}-48 x^{8}+216 c_1 \,x^{4}-768 x^{3}+81 c_1^{2}}\right )^{{1}/{3}}} \\
y &= \frac {\left (i \sqrt {3}-1\right ) \left (-144 x^{4}-108 c_1 -8 x^{9}+12 \sqrt {12 c_1 \,x^{9}-48 x^{8}+216 c_1 \,x^{4}-768 x^{3}+81 c_1^{2}}\right )^{{1}/{3}}}{12}-\frac {\left (x^{2} \left (-144 x^{4}-108 c_1 -8 x^{9}+12 \sqrt {12 c_1 \,x^{9}-48 x^{8}+216 c_1 \,x^{4}-768 x^{3}+81 c_1^{2}}\right )^{{1}/{3}}+\left (1+i \sqrt {3}\right ) \left (x^{5}+12\right )\right ) x}{3 \left (-144 x^{4}-108 c_1 -8 x^{9}+12 \sqrt {12 c_1 \,x^{9}-48 x^{8}+216 c_1 \,x^{4}-768 x^{3}+81 c_1^{2}}\right )^{{1}/{3}}} \\
\end{align*}
✓ Mathematica. Time used: 5.695 (sec). Leaf size: 512
ode=( 3*x^2*y[x]^2 -4*y[x] )+( 3*y[x]^2 -4*x +2*x^3*y[x] )*D[y[x],{x,1}]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \frac {1}{6} \left (-2 x^3+2^{2/3} \sqrt [3]{-2 x^9-36 x^4+3 \sqrt {3} \sqrt {-4 c_1 x^9-16 x^8-72 c_1 x^4-256 x^3+27 c_1{}^2}+27 c_1}+\frac {2 \sqrt [3]{2} \left (x^5+12\right ) x}{\sqrt [3]{-2 x^9-36 x^4+3 \sqrt {3} \sqrt {-4 c_1 x^9-16 x^8-72 c_1 x^4-256 x^3+27 c_1{}^2}+27 c_1}}\right )\\ y(x)&\to \frac {1}{12} \left (-4 x^3+i 2^{2/3} \left (\sqrt {3}+i\right ) \sqrt [3]{-2 x^9-36 x^4+3 \sqrt {3} \sqrt {-4 c_1 x^9-16 x^8-72 c_1 x^4-256 x^3+27 c_1{}^2}+27 c_1}-\frac {2 i \sqrt [3]{2} \left (\sqrt {3}-i\right ) \left (x^5+12\right ) x}{\sqrt [3]{-2 x^9-36 x^4+3 \sqrt {3} \sqrt {-4 c_1 x^9-16 x^8-72 c_1 x^4-256 x^3+27 c_1{}^2}+27 c_1}}\right )\\ y(x)&\to \frac {1}{12} \left (-4 x^3-2^{2/3} \left (1+i \sqrt {3}\right ) \sqrt [3]{-2 x^9-36 x^4+3 \sqrt {3} \sqrt {-4 c_1 x^9-16 x^8-72 c_1 x^4-256 x^3+27 c_1{}^2}+27 c_1}+\frac {2 i \sqrt [3]{2} \left (\sqrt {3}+i\right ) \left (x^5+12\right ) x}{\sqrt [3]{-2 x^9-36 x^4+3 \sqrt {3} \sqrt {-4 c_1 x^9-16 x^8-72 c_1 x^4-256 x^3+27 c_1{}^2}+27 c_1}}\right ) \end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(3*x**2*y(x)**2 + (2*x**3*y(x) - 4*x + 3*y(x)**2)*Derivative(y(x), x) - 4*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out