25.3.4 problem 5.2

Internal problem ID [6869]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 4
Problem number : 5.2
Date solved : Tuesday, September 30, 2025 at 03:58:52 PM
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: 0.156 (sec). Leaf size: 40

ode:=8*y(x)+10*x+(5*y(x)+7*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \operatorname {RootOf}\left (x^{5} c_1 \,\textit {\_Z}^{25}-2 x^{5} c_1 \,\textit {\_Z}^{20}+x^{5} c_1 \,\textit {\_Z}^{15}-1\right )^{5}-2 x \]

✓ Mathematica. Time used: 2.524 (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: 0.456 (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)
 

\[ \log {\left (x \right )} = C_{1} - \log {\left (\left (1 + \frac {y{\left (x \right )}}{x}\right )^{\frac {2}{5}} \left (2 + \frac {y{\left (x \right )}}{x}\right )^{\frac {3}{5}} \right )} \]