69.12.16 problem 290

Internal problem ID [18169]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 290
Date solved : Thursday, October 02, 2025 at 03:06:44 PM
CAS classification : [_separable]

\begin{align*} y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=diff(y(x),x)*(3*x^2-2*x)-y(x)*(6*x-2) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 x \left (3 x -2\right ) \]

✓ Mathematica. Time used: 0.072 (sec). Leaf size: 42

ode=D[y[x],x]*(3*x^2-2*x)-y[x]*(6*x-2)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \exp \left (\int _1^x\frac {2-6 K[1]}{2 K[1]-3 K[1]^2}dK[1]\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.234 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2 - 6*x)*y(x) + (3*x**2 - 2*x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x \left (3 x - 2\right ) \]