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Solve the given differential equation.$$\frac{d y}{d x}=\frac{\left(x^{3}+3\right) y^{2}}{x^{4}\left(y^{3}+8\right)}$$

$$x^{3} y^{3}-16 x^{3}=2 x^{3} y \ln |x|-2 y+c x^{3} y$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 2

Applications of Antidifferentiation

Integrals

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Idaho State University

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.

40:35

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.

04:28

Solve the given differenti…

01:52

04:23

01:02

the given equation we redid amounts diva learned last. All right equals You drive to the par -3. Now this is a Bernoulli equation you know, standard from has given us these are by the last B in Taiwan. You and do what? And we're being years old. Excellent beeping forex and kill me. It really is minus not to solve this. I mean Solution. We used to wipe our 1- and which is all right. We have a baby. I want to be in Yeah. Or like you do you like the multiply creation one right? Or like you do you remember? Yes. You mean like the hopes for what? Yeah, says devi my dear last I mean mhm. Yes. Mhm. Right now this is a linear equation. We know that the linearity has the standard from the rebranding. Yes. Even into we need you won The P one is 16 XQ one is 32 works both being functions the long all this before indeed in fact over. Mhm. DeParle the one being come with us immigration. Do you know the year? Yes. Yeah. Uh huh. Multiplied into the integrating exactly this. E mm correct. DVs and then Right. Yeah. Need to be a texas square into the right Okay people it's all right. This is nothing but the by the exhaust V into E power A texas right little X. And keep our IT. Now let's integrate both sides. We get we into you follow right equal stew integration two you brother. This is where let's assume be as he takes as well. We get DT my dear. Uh huh. Dina this integration victims the world the power the the comes us to keep our steve Yeah. You two x squared of me. Yes. Why powerful equals two two. No, he he power minus no.

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