30.4.16 problem 17
Internal
problem
ID
[7499]
Book
:
Fundamentals
of
Differential
Equations.
By
Nagle,
Saff
and
Snider.
9th
edition.
Boston.
Pearson
2018.
Section
:
Chapter
2,
First
order
differential
equations.
Section
2.5,
Special
Integrating
Factors.
Exercises.
page
69
Problem
number
:
17
Date
solved
:
Sunday, October 12, 2025 at 01:34:43 AM
CAS
classification
:
[_rational, [_Abel, `2nd type`, `class B`]]
\begin{align*} 2 x +2 y+2 x^{3} y+4 x^{2} y^{2}+\left (2 x +x^{4}+2 x^{3} y\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.005 (sec). Leaf size: 27
ode:=2*x+2*y(x)+2*x^3*y(x)+4*x^2*y(x)^2+(2*x+x^4+2*x^3*y(x))*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {-\frac {x^{3}}{2}+\operatorname {LambertW}\left (-2 x c_1 \,{\mathrm e}^{-1+\frac {x^{3}}{2}}\right )}{x^{2}}
\]
✓ Mathematica. Time used: 8.199 (sec). Leaf size: 508
ode=(2*x+2*y[x]+2*x^3*y[x]+4*x^2*y[x]^2 )+( 2*x+x^4+2*x^3*y[x] )*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\frac {\left (3 x^3+2\right ) \left (x^3+2 \log (x)\right )}{9 \sqrt [3]{2} \sqrt [3]{-\left (3 x^3+2\right )^3}}=\frac {\sqrt [3]{-2} \left ((-2)^{2/3}-\frac {\left (3 x^3+2\right ) \left (x^3+2 x^2 y(x)-4\right )}{\sqrt [3]{2} \sqrt [3]{-\left (3 x^3+2\right )^3} \left (x^3+2 x^2 y(x)+2\right )}\right ) \left (\frac {2^{2/3} \left (3 x^3+2\right ) \left (x^3+2 x^2 y(x)-4\right )}{\sqrt [3]{-\left (3 x^3+2\right )^3} \left (x^3+2 x^2 y(x)+2\right )}+(-2)^{2/3}\right ) \left (\left (1-\frac {\sqrt [3]{-1} \left (3 x^3+2\right ) \left (x^3+2 x^2 y(x)-4\right )}{\sqrt [3]{-\left (3 x^3+2\right )^3} \left (x^3+2 x^2 y(x)+2\right )}\right ) \log \left (2 (-2)^{2/3}-\frac {2^{2/3} \left (3 x^3+2\right ) \left (x^3+2 x^2 y(x)-4\right )}{\sqrt [3]{-\left (3 x^3+2\right )^3} \left (x^3+2 x^2 y(x)+2\right )}\right )-\left (1-\frac {\sqrt [3]{-1} \left (3 x^3+2\right ) \left (x^3+2 x^2 y(x)-4\right )}{\sqrt [3]{-\left (3 x^3+2\right )^3} \left (x^3+2 x^2 y(x)+2\right )}\right ) \log \left (\frac {2^{2/3} \left (3 x^3+2\right ) \left (x^3+2 x^2 y(x)-4\right )}{\sqrt [3]{-\left (3 x^3+2\right )^3} \left (x^3+2 x^2 y(x)+2\right )}+(-2)^{2/3}\right )+3\right )}{9 \left (\frac {\left (x^3+2 x^2 y(x)-4\right )^3}{\left (x^3+2 x^2 y(x)+2\right )^3}-\frac {3 \sqrt [3]{-1} \left (3 x^3+2\right ) \left (x^3+2 x^2 y(x)-4\right )}{\sqrt [3]{-\left (3 x^3+2\right )^3} \left (x^3+2 x^2 y(x)+2\right )}+2\right )}+c_1,y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(2*x**3*y(x) + 4*x**2*y(x)**2 + 2*x + (x**4 + 2*x**3*y(x) + 2*x)*Derivative(y(x), x) + 2*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out