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Numerade Educator

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Problem 7 Medium Difficulty

Solve the differential equation.
$ \frac {d \theta}{dt} = \frac {t \sec \theta}{\theta e^{t^2}} $

Answer

$\theta \sin \theta+\cos \theta=-\frac{1}{2} e^{-t^{2}}+C$

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Video Transcript

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.