6.6.6 problem 6
Internal
problem
ID
[1685]
Book
:
Elementary
differential
equations
with
boundary
value
problems.
William
F.
Trench.
Brooks/Cole
2001
Section
:
Chapter
2,
First
order
equations.
Exact
equations.
Section
2.5
Page
79
Problem
number
:
6
Date
solved
:
Tuesday, September 30, 2025 at 05:00:39 AM
CAS
classification
:
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 4 x +7 y+\left (3 x +4 y\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.021 (sec). Leaf size: 28
ode:=4*x+7*y(x)+(3*x+4*y(x))*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {-2 c_1 x +\operatorname {RootOf}\left (-3 x c_1 \,\textit {\_Z}^{5}+2 \textit {\_Z}^{6}-1\right )}{c_1}
\]
✓ Mathematica. Time used: 4.006 (sec). Leaf size: 409
ode=(4*x+7*y[x])+(3*x+4*y[x])*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,1\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,2\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,3\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,4\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,5\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,6\right ] \end{align*}
✓ Sympy. Time used: 0.489 (sec). Leaf size: 27
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(4*x + (3*x + 4*y(x))*Derivative(y(x), x) + 7*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\log {\left (x \right )} = C_{1} - \log {\left (\sqrt [6]{\frac {1}{2} + \frac {y{\left (x \right )}}{x}} \left (2 + \frac {y{\left (x \right )}}{x}\right )^{\frac {5}{6}} \right )}
\]