69.7.11 problem 186

Internal problem ID [18091]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 7, Total differential equations. The integrating factor. Exercises page 61
Problem number : 186
Date solved : Thursday, October 02, 2025 at 02:41:41 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 1.285 (sec). Leaf size: 5

ode:=2/y(x)^3*x+(y(x)^2-3*x^2)/y(x)^4*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x \]

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 43

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]^2-3}{(K[1]-1) K[1] (K[1]+1)}dK[1]=-\log (x),y(x)\right ] \]

✗ Sympy

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

Timed Out