60.1.531 problem 544

Internal problem ID [10545]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 544
Date solved : Sunday, March 30, 2025 at 05:57:03 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5}&=0 \end{align*}

✓ Maple. Time used: 2.549 (sec). Leaf size: 4602

ode:=x^7*y(x)^2*diff(y(x),x)^3-(3*x^6*y(x)^3-1)*diff(y(x),x)^2+3*x^5*y(x)^4*diff(y(x),x)-x^4*y(x)^5 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {2^{{2}/{3}}}{3 x^{2}} \\ y &= -\frac {2^{{2}/{3}} \left (1+i \sqrt {3}\right )}{6 x^{2}} \\ y &= \frac {2^{{2}/{3}} \left (i \sqrt {3}-1\right )}{6 x^{2}} \\ y &= 0 \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Mathematica. Time used: 2.075 (sec). Leaf size: 80

ode=-(x^4*y[x]^5) + 3*x^5*y[x]^4*D[y[x],x] - (-1 + 3*x^6*y[x]^3)*D[y[x],x]^2 + x^7*y[x]^2*D[y[x],x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \sqrt [3]{c_1 x^3+c_1{}^{2/3}} \\ y(x)\to 0 \\ y(x)\to \frac {(-2)^{2/3}}{3 x^2} \\ y(x)\to \frac {2^{2/3}}{3 x^2} \\ y(x)\to -\frac {\sqrt [3]{-1} 2^{2/3}}{3 x^2} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**7*y(x)**2*Derivative(y(x), x)**3 + 3*x**5*y(x)**4*Derivative(y(x), x) - x**4*y(x)**5 - (3*x**6*y(x)**3 - 1)*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out