63.1.54 problem 73

Internal problem ID [15494]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 73
Date solved : Thursday, October 02, 2025 at 10:18:47 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} y-3 x^{2}-\left (4 y-x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 47

ode:=y(x)-3*x^2-(4*y(x)-x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {x}{4}-\frac {\sqrt {-8 x^{3}+x^{2}+8 c_1}}{4} \\ y &= \frac {x}{4}+\frac {\sqrt {-8 x^{3}+x^{2}+8 c_1}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 67

ode=(y[x]-3*x^2)-(4*y[x]-x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} \left (x-i \sqrt {8 x^3-x^2-16 c_1}\right )\\ y(x)&\to \frac {1}{4} \left (x+i \sqrt {8 x^3-x^2-16 c_1}\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**2 - (-x + 4*y(x))*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out