87.6.7 problem 7
Internal
problem
ID
[23324]
Book
:
Ordinary
differential
equations
with
modern
applications.
Ladas,
G.
E.
and
Finizio,
N.
Wadsworth
Publishing.
California.
1978.
ISBN
0-534-00552-7.
QA372.F56
Section
:
Chapter
1.
Elementary
methods.
First
order
differential
equations.
Exercise
at
page
53
Problem
number
:
7
Date
solved
:
Thursday, October 02, 2025 at 09:37:05 PM
CAS
classification
:
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 3 y+\left (7 x -y\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.002 (sec). Leaf size: 16
ode:=3*y(x)+(7*x-y(x))*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
x -\frac {y}{10}-\frac {c_1}{y^{{7}/{3}}} = 0
\]
✓ Mathematica. Time used: 4.91 (sec). Leaf size: 436
ode=3*y[x]+(7*x-y[x])*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \text {Root}\left [\text {$\#$1}^{10}-30 \text {$\#$1}^9 x+300 \text {$\#$1}^8 x^2-1000 \text {$\#$1}^7 x^3+e^{10 c_1}\&,1\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^{10}-30 \text {$\#$1}^9 x+300 \text {$\#$1}^8 x^2-1000 \text {$\#$1}^7 x^3+e^{10 c_1}\&,2\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^{10}-30 \text {$\#$1}^9 x+300 \text {$\#$1}^8 x^2-1000 \text {$\#$1}^7 x^3+e^{10 c_1}\&,3\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^{10}-30 \text {$\#$1}^9 x+300 \text {$\#$1}^8 x^2-1000 \text {$\#$1}^7 x^3+e^{10 c_1}\&,4\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^{10}-30 \text {$\#$1}^9 x+300 \text {$\#$1}^8 x^2-1000 \text {$\#$1}^7 x^3+e^{10 c_1}\&,5\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^{10}-30 \text {$\#$1}^9 x+300 \text {$\#$1}^8 x^2-1000 \text {$\#$1}^7 x^3+e^{10 c_1}\&,6\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^{10}-30 \text {$\#$1}^9 x+300 \text {$\#$1}^8 x^2-1000 \text {$\#$1}^7 x^3+e^{10 c_1}\&,7\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^{10}-30 \text {$\#$1}^9 x+300 \text {$\#$1}^8 x^2-1000 \text {$\#$1}^7 x^3+e^{10 c_1}\&,8\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^{10}-30 \text {$\#$1}^9 x+300 \text {$\#$1}^8 x^2-1000 \text {$\#$1}^7 x^3+e^{10 c_1}\&,9\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^{10}-30 \text {$\#$1}^9 x+300 \text {$\#$1}^8 x^2-1000 \text {$\#$1}^7 x^3+e^{10 c_1}\&,10\right ]\\ y(x)&\to 0 \end{align*}
✓ Sympy. Time used: 0.406 (sec). Leaf size: 19
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((7*x - y(x))*Derivative(y(x), x) + 3*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\log {\left (y{\left (x \right )} \right )} = C_{1} - \log {\left (\left (\frac {10 x}{y{\left (x \right )}} - 1\right )^{\frac {3}{10}} \right )}
\]