31.3.4 problem 5.2
Internal
problem
ID
[5734]
Book
:
Differential
Equations,
By
George
Boole
F.R.S.
1865
Section
:
Chapter
4
Problem
number
:
5.2
Date
solved
:
Sunday, March 30, 2025 at 10:06:42 AM
CAS
classification
:
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 8 y+10 x +\left (5 y+7 x \right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.203 (sec). Leaf size: 38
ode:=8*y(x)+10*x+(5*y(x)+7*x)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = x \left (-2+\operatorname {RootOf}\left (x^{5} c_1 \,\textit {\_Z}^{25}-2 x^{5} c_1 \,\textit {\_Z}^{20}+x^{5} c_1 \,\textit {\_Z}^{15}-1\right )^{5}\right )
\]
✓ Mathematica. Time used: 2.285 (sec). Leaf size: 276
ode=(8*y[x]+10*x)+(5*y[x]+7*x)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,1\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,2\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,3\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,4\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,5\right ] \\
\end{align*}
✓ Sympy. Time used: 0.706 (sec). Leaf size: 26
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(10*x + (7*x + 5*y(x))*Derivative(y(x), x) + 8*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\log {\left (x \right )} = C_{1} - \log {\left (\left (1 + \frac {y{\left (x \right )}}{x}\right )^{\frac {2}{5}} \left (2 + \frac {y{\left (x \right )}}{x}\right )^{\frac {3}{5}} \right )}
\]