62.12.16 problem Ex 17

Internal problem ID [12791]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number : Ex 17
Date solved : Monday, March 31, 2025 at 07:07:47 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} 5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.393 (sec). Leaf size: 48

ode:=5*x*y(x)-3*y(x)^3+(3*x^2-7*x*y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{\operatorname {RootOf}\left (c_1 \,\textit {\_Z}^{7}-x^{{5}/{2}} \textit {\_Z}^{4}+x^{{3}/{2}}\right )^{2}} \\ y &= \frac {1}{\operatorname {RootOf}\left (c_1 \,\textit {\_Z}^{7}+x^{{5}/{2}} \textit {\_Z}^{4}-x^{{3}/{2}}\right )^{2}} \\ \end{align*}

✓ Mathematica. Time used: 4.798 (sec). Leaf size: 288

ode=(5*x*y[x]-3*y[x]^3)+(3*x^2-7*x*y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,1\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,2\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,3\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,4\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,5\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,6\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,7\right ] \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*x*y(x) + (3*x**2 - 7*x*y(x)**2)*Derivative(y(x), x) - 3*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-5*x + 3*y(x)**2)*y(x)/(x*(3*x - 7*y(x)**2)) cannot be solved by the factorable group method