77.1.64 problem 83 (page 120)

Internal problem ID [17883]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 83 (page 120)
Date solved : Monday, March 31, 2025 at 04:48:01 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 77

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

\begin{align*} -\frac {c_1}{\sqrt {-x -\sqrt {x^{2}-2 y}}}+\frac {2 x}{3}-\frac {\sqrt {x^{2}-2 y}}{3} &= 0 \\ -\frac {c_1}{\sqrt {-x +\sqrt {x^{2}-2 y}}}+\frac {2 x}{3}+\frac {\sqrt {x^{2}-2 y}}{3} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 60.167 (sec). Leaf size: 1000

ode=D[y[x],x]^2+2*x*D[y[x],x]+2*y[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*y(x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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