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Solve the given differential equation.$$\frac{d y}{d x}=3 x^{2} y^{2}$$

$$y=-\frac{1}{x^{3}+c}$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 2

Applications of Antidifferentiation

Integrals

Missouri State University

Baylor University

University of Nottingham

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

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In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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Solve the given differenti…

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Solve the differential equ…

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we want to solve the given differential equation. Dy dx is equal to three X squared y square. A differential equation such as this one can be solved by multiple efforts specifically, since we can isolate Y and X on either side of this equation easily we're going to solve this differential equation by means of separation of variables. So first, let's isolate our variables on either side of the equation. This gives dy over wide square is equal to three X squared dx. Next we integrate integration gives integral. Dy over Y squared equals integral. Three X squared dx on the right gives this gives us negative one over Y equals X cubed plus C. Where C is our constant immigration. We want to solve this differential equation in terms of why? So if we multiply both sides by negative one and take the inverse, we have final result. Why is equal to negative one over X cubed plus C.

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