dy/dx=4x^3y-3x^2y

Question

dy/dx=4x^3y-3x^2y

kainui · Answer

This is a separable differential equation. Factor out a y on the right side and divide both sides by y then multiply both sides by dx and integrate both sides with respect to their own variables. Don't forget the +C.

anonymous · Answer

The answer comes in  a form of Me^x^4-x^3  .

anonymous · Answer

M being any real number that is not 0

freckles · Answer

Right e^c is never 0 for any real number c

freckles · Answer

Don't forget law of exponents here

tkhunny · Answer

Please use parentheses to clarify intent.

Me^x^4-x^3 <== This is horrible.  You should have studied the Order of Operations.  You should not be in Differential Equations lacking this information.  Maybe you were just being loose and informal.  Don't do that.

dy/dx=4x^3y-3x^2y

$\dfrac{dy}{dx} = 4x^{3}y - 3x^{2}y$

$dy/y = 4x^{3} - 3x^{2}dx$

$ln|y| = x^{4} - x^{3} + C$

$|y| = e^{x^{4} - x^{3} + C}$

$|y| = Me^{x^{4} - x^{3}}$, where $M = e^{C}$, but no one cares.  It's still just an arbitrary constant.

Be careful and be clear.

precal · Answer

Nice job @tkhunny