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Solve the differential equation.$ \frac {dp}{dt} = t^2 - p + t^2 - 1 $

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$$p=K e^{t^{3} / 3-t}-1$$

Calculus 2 / BC

Chapter 9

Differential Equations

Section 3

Separable Equations

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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Solve the differential equ…

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Solve the given differenti…

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Solve the following differ…

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this question asks us to solve the differential equation. DP over. GT is T squared P minus P plus T squared minus one. Okay, first up, let's put stuff into factored forms than we can cancel off terms. Soapy times T squared, minus wanna is our first part. And then we obviously can't factor t squared minus one with any more variables. Now we want all the peace stuff in the left hand side and all the t's stuff on the right hand side. So do some manipulation. So you have dp over people. Swan, the left hand side on that T squared minus one D two. On the right hand side, it is very important that we put each variable on separate sides so we cannot integrate on the left hand side, we have natural log of people swan. And then we have minus natural FCC being our constant of integration is equivalent to we had t squared them, increase the exploited by one divide by the new exponents on the negative one integrates to negative t This simplifies to people's one oversee is e to the T cubed minus three t divide by three. And then lastly we want to see on the right hand side. So we have people. Swan. There is multiplying both sides by the sea in order to get our final simplifying solution.

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