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Find the solution of the differential equation that satisfies the given initial condition.$ x \ln x = y(1 + \sqrt {3 + y^2}) y', y(1) = 1 $

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Calculus 2 / BC

Chapter 9

Differential Equations

Section 3

Separable Equations

Oregon State University

Baylor University

University of Nottingham

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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Find the solution of the d…

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solve the following differ…

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Find the general solution …

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Solve the given differenti…

this question asked us to find the solution of the differential equation that satisfies the given initial condition. We know that what we're gonna want to do is put all the left him terms on the left hand side, involving acts and then all the terms involving why on the right hand side, we can split up. Why do you why plus y squared of three y squared And then we know that we have the white, the end. Therefore, we can integrate each of thes three parts separately to give us X squared over to cause X integrates to export over too. And then we have plus C cause we're integrating. Now we know that why have one is one has given the problem. Therefore, we know we can plug in. Why have one is one to give us a sea of negative 41 divided by 12. Therefore, our final solution is the exact same equation we figured out in the previous slide. But instead of pussy, we're gonna be playing in what C is, and it's negative

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