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What is a solution to the differential equation #dy/dx=(x^2+2)/(4y^3)#?

Answer 1

Christopher Allers

#y = pm root4(x^3/3+2x + C) #

#dy/dx=(x^2+2)/(4y^3)#

this is separable

#4y^3 dy/dx=x^2+2#

#int \ 4y^3 dy/dx \ dx=int \ x^2+2 \ dx#

#int \ 4y^3 \ dy =int \ x^2+2 \ dx#

#y^4 = x^3/3+2x + C #

#y = pm root4(x^3/3+2x + C) #

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Answer 2

Samantha Adkison

The solution to the differential equation ( \frac{{dy}}{{dx}} = \frac{{x^2 + 2}}{{4y^3}} ) can be found by separating variables and integrating. The general solution is given by ( y(x) = \sqrt[4]{\frac{{x^4}}{4} + C} ), where ( C ) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.