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Solve the differential equation.$ \frac {d \theta}{dt} = \frac {t \sec \theta}{\theta e^{t^2}} $
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Calculus 2 / BC
Chapter 9
Differential Equations
Section 3
Separable Equations
Missouri 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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this question asked us to solve the differential equation. We know that we have teeth. Data over DT is too secret Data divide by Breda e to the T Square. No, What we know we need to do is we know we want all that they doesn't left inside and all the cheese on the right hand side. So multiply both sides by data to get rid of that data on the right and bring it over to the left. Simple five. We know one over seeking is the same thing as co sign and then this. We can write this with the negative exponents like this. No, we know we're gonna be taking the integral of both sides. As you can see over here, this is the first integral sign this second integral sign. You can do this by using the formula for integration by parts. All right, it over here. Given the fact that you is negative, cheese squared. I get to d t. As now you're to t d g is do you and then t d t is negative 1/2. Do you? We know we can use integration by parts to do negative 1/2 times the integral of heat of the U. D you, which gives us negative 1/2 feet of the you pussy. Now, last step, you needs to be substituted in so back. Substitute. Negative 1/2 e. Remember, you was actually negative, Chief scored. So we're literally just plug in your end and this is our final solution.
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