23.2.313 problem 336

Internal problem ID [5668]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 336
Date solved : Tuesday, September 30, 2025 at 01:40:44 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.347 (sec). Leaf size: 399

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

\begin{align*} y(x)&\to -\sqrt {c_1 \left (x^2+\frac {1}{1+c_1{}^2}\right )}\\ y(x)&\to \sqrt {c_1 \left (x^2+\frac {1}{1+c_1{}^2}\right )}\\ y(x)&\to -\frac {\sqrt [4]{-8 x^4+20 x^2-\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}}\\ y(x)&\to -\frac {i \sqrt [4]{-8 x^4+20 x^2-\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}}\\ y(x)&\to \frac {i \sqrt [4]{-8 x^4+20 x^2-\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}}\\ y(x)&\to \frac {\sqrt [4]{-8 x^4+20 x^2-\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}}\\ y(x)&\to -\frac {\sqrt [4]{-8 x^4+20 x^2+\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}}\\ y(x)&\to -\frac {i \sqrt [4]{-8 x^4+20 x^2+\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}}\\ y(x)&\to \frac {i \sqrt [4]{-8 x^4+20 x^2+\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}}\\ y(x)&\to \frac {\sqrt [4]{-8 x^4+20 x^2+\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}} \end{align*}

✗ Sympy

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

Timed Out