69.12.38 problem 312

Internal problem ID [18191]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 312
Date solved : Thursday, October 02, 2025 at 03:08:49 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} 4 {y^{\prime }}^{2} x^{2}-y^{2}&=x y^{3} \end{align*}

✓ Maple. Time used: 1.536 (sec). Leaf size: 1759

ode:=4*x^2*diff(y(x),x)^2-y(x)^2 = x*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Mathematica. Time used: 105.357 (sec). Leaf size: 1401

ode=4*x^2*D[y[x],x]^2-y[x]^2==x*y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✓ Sympy. Time used: 2.329 (sec). Leaf size: 105

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

\[ \left [ - \log {\left (x \right )} - \frac {8 \log {\left (\sqrt {x y{\left (x \right )} + 1} - 2 \right )}}{3} + 2 \log {\left (\sqrt {x y{\left (x \right )} + 1} - 1 \right )} + \frac {2 \log {\left (\sqrt {x y{\left (x \right )} + 1} + 1 \right )}}{3} = C_{1}, \ - \log {\left (x \right )} + \frac {2 \log {\left (\sqrt {x y{\left (x \right )} + 1} - 1 \right )}}{3} + 2 \log {\left (\sqrt {x y{\left (x \right )} + 1} + 1 \right )} - \frac {8 \log {\left (\sqrt {x y{\left (x \right )} + 1} + 2 \right )}}{3} = C_{1}\right ] \]