69.1.62 problem 89

Internal problem ID [14144]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 89
Date solved : Monday, March 31, 2025 at 12:10:39 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 642

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

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

✓ Mathematica. Time used: 60.148 (sec). Leaf size: 931

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

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