63.1.53 problem 72

Internal problem ID [15493]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 72
Date solved : Thursday, October 02, 2025 at 10:18:46 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {x}{2}-\frac {\sqrt {12 x^{3}+9 x^{2}+36 c_1}}{6} \\ y &= \frac {x}{2}+\frac {\sqrt {12 x^{3}+9 x^{2}+36 c_1}}{6} \\ \end{align*}

✓ Mathematica. Time used: 0.097 (sec). Leaf size: 81

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

\begin{align*} y(x)&\to \frac {1}{6} \left (3 x-i \sqrt {3} \sqrt {-4 x^3-3 x^2-12 c_1}\right )\\ y(x)&\to \frac {1}{6} \left (3 x+i \sqrt {3} \sqrt {-4 x^3-3 x^2-12 c_1}\right ) \end{align*}

✗ Sympy

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

Timed Out