Solve The Differential Equation. Dy Dx = 6x2y2 Repack Jun 2026

y=-12x3+Cy equals the fraction with numerator negative 1 and denominator 2 x cubed plus cap C end-fraction Final Answer The general solution to the differential equation is is the constant of integration.

$$ \frac{dy}{dx} = f(x)g(y) $$

Using the power rule for $x$: $$ \int 6x^2 , dx = 6 \left( \frac{x^3}{3} \right) = 2x^3 $$ solve the differential equation. dy dx = 6x2y2

import sympy x = sympy.symbols('x') y = sympy.symbols('y', cls=sympy.Function) # Define the differential equation: dy/dx = 6*x^2*y^2 diffeq = sympy.Equality(y(x).diff(x), 6 * x**2 * y(x)**2) # Solve the differential equation solution = sympy.dsolve(diffeq, y(x)) print(solution) Use code with caution. Copied to clipboard y=-12x3+Cy equals the fraction with numerator negative 1