77.1.77 problem 96 (page 135)

Internal problem ID [17896]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 96 (page 135)
Date solved : Monday, March 31, 2025 at 04:49:04 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out