77.1.101 problem 129 (page 179)

Internal problem ID [17920]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 129 (page 179)
Date solved : Monday, March 31, 2025 at 04:51:28 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} {y^{\prime \prime }}^{2}+2 x y^{\prime \prime }-y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.330 (sec). Leaf size: 1867

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 132.325 (sec). Leaf size: 1045

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -(2*x + Derivative(y(x), (x, 2)))*Derivative(y(x), (x, 2)) + Derivative(y(x), x) cannot be solved by the factorable group method