75.12.11 problem 285

Internal problem ID [16806]
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 : 285
Date solved : Monday, March 31, 2025 at 03:21:56 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

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

\begin{align*} y &= \sqrt {x^{2}+c_1}\, x \\ y &= -\sqrt {x^{2}+c_1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.189 (sec). Leaf size: 34

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

\begin{align*} y(x)\to -x \sqrt {x^2+c_1} \\ y(x)\to x \sqrt {x^2+c_1} \\ \end{align*}

✓ Sympy. Time used: 0.351 (sec). Leaf size: 26

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

\[ \left [ y{\left (x \right )} = - x \sqrt {C_{1} + x^{2}}, \ y{\left (x \right )} = x \sqrt {C_{1} + x^{2}}\right ] \]