75.11.6 problem 265

Internal problem ID [16778]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 11. Singular solutions of differential equations. Exercises page 92
Problem number : 265
Date solved : Thursday, March 13, 2025 at 08:45:21 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.089 (sec). Leaf size: 65

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

\begin{align*} y &= -\frac {x^{5}}{4} \\ y &= \frac {c_{1} \left (x^{3}+c_{1} \right )}{x} \\ y &= \frac {c_{1} \left (-x^{3}+c_{1} \right )}{x} \\ y &= \frac {c_{1} \left (-x^{3}+c_{1} \right )}{x} \\ y &= \frac {c_{1} \left (x^{3}+c_{1} \right )}{x} \\ \end{align*}

✓ Mathematica. Time used: 1.893 (sec). Leaf size: 94

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

\begin{align*} y(x)\to -\frac {i (\cosh (3 c_1)+\sinh (3 c_1)) \left (x^3-i \cosh (3 c_1)-i \sinh (3 c_1)\right )}{x} \\ y(x)\to \frac {i (\cosh (3 c_1)+\sinh (3 c_1)) \left (x^3+i \cosh (3 c_1)+i \sinh (3 c_1)\right )}{x} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

Timed Out