85.35.3 problem 4
Internal
problem
ID
[22723]
Book
:
Applied
Differential
Equations.
By
Murray
R.
Spiegel.
3rd
edition.
1980.
Pearson.
ISBN
978-0130400970
Section
:
Chapter
two.
First
order
and
simple
higher
order
ordinary
differential
equations.
C
Exercises
at
page
68
Problem
number
:
4
Date
solved
:
Thursday, October 02, 2025 at 09:13:53 PM
CAS
classification
:
[[_homogeneous, `class G`], _rational]
\begin{align*} x^{2} y+2 y^{4}+\left (x^{3}+3 x y^{3}\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.226 (sec). Leaf size: 37
ode:=x^2*y(x)+2*y(x)^4+(x^3+3*x*y(x)^3)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
\ln \left (x \right )-c_1 +\frac {\ln \left (\frac {12 y^{3}+5 x^{2}}{x^{2}}\right )}{20}+\frac {3 \ln \left (\frac {y}{x^{{2}/{3}}}\right )}{5} = 0
\]
✓ Mathematica. Time used: 60.083 (sec). Leaf size: 621
ode=(x^2*y[x]+2*y[x]^4)+(x^3+3*x*y[x]^3)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,1\right ]}\\ y(x)&\to -\sqrt [3]{-1} \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,1\right ]}\\ y(x)&\to (-1)^{2/3} \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,1\right ]}\\ y(x)&\to \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,2\right ]}\\ y(x)&\to -\sqrt [3]{-1} \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,2\right ]}\\ y(x)&\to (-1)^{2/3} \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,2\right ]}\\ y(x)&\to \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,3\right ]}\\ y(x)&\to -\sqrt [3]{-1} \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,3\right ]}\\ y(x)&\to (-1)^{2/3} \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,3\right ]}\\ y(x)&\to \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,4\right ]}\\ y(x)&\to -\sqrt [3]{-1} \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,4\right ]}\\ y(x)&\to (-1)^{2/3} \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,4\right ]}\\ y(x)&\to \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,5\right ]}\\ y(x)&\to -\sqrt [3]{-1} \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,5\right ]}\\ y(x)&\to (-1)^{2/3} \sqrt [3]{\text {Root}\left [-12 \text {$\#$1}^5-5 \text {$\#$1}^4 x^2+\frac {e^{20 c_1}}{x^{10}}\&,5\right ]} \end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x**2*y(x) + (x**3 + 3*x*y(x)**3)*Derivative(y(x), x) + 2*y(x)**4,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2 - 2*y(x)**3)*y(x)/(x*(x**2 + 3*y(x)