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Verify that the given function y is a solution of the differential equation that follows it. Assume that C is an arbitrary constant:y(t) = Ce 8t; y' (t) - 8y(t...

Question

Verify that the given function y is a solution of the differential equation that follows it. Assume that C is an arbitrary constant:y(t) = Ce 8t; y' (t) - 8y(t) = 0Start by substituting y(t) =. Ce 8t into the second half of the equation:y' (t)=0Next find the derivative of y(t) = Ce 8t .y' (t) =Simplify the equation for the given function: Is the given function a solution for the differential equation?0A Yes because when y andy are substituted into the equation, the result is a tru

Verify that the given function y is a solution of the differential equation that follows it. Assume that C is an arbitrary constant: y(t) = Ce 8t; y' (t) - 8y(t) = 0 Start by substituting y(t) =. Ce 8t into the second half of the equation: y' (t) =0 Next find the derivative of y(t) = Ce 8t . y' (t) = Simplify the equation for the given function: Is the given function a solution for the differential equation? 0A Yes because when y andy are substituted into the equation, the result is a true statement. Yes because the given function equals 0, so the original function must satisfy the initial value problem. No because when y and y' are substituted into the equation; the result is not a true statement: No because the given function does not equal 0, so the original function cannot satisfy the initial value problem



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Verify that the given function y is a solution of the differential equation that follows it. Assume that $C$ is an arbitrary constant. $$y(t)=C t^{-3} ; t y^{\prime}(t)+3 y(t)=0$$

They asked us to verify that it satisfies the central vision for Let's Find the first year all of negatives he wanted for the negative to be for the X. We take our second riveted and we'll have C one e to the negative. We'll see to be to the X notices. The same thing someone has attracted him. One from me of it well, under 10 does satisfy the differential equation.

Here. We have to verify that the given function you off t is equals toe. See, even it'll party bless C two times d you do about would be Is the solution off the differential equation which is you? Double prime tea minus two. You prime d bless you off t is equals to zero. Now we can write this differential equation in this field so that you double prime tea as equals to you. Prime tea on headed his minus you off. No, First of all will calculate you prime tea and then we'll calculate you double prime tea and then replied, the very loose in this equation. So you prime tea will be quotes to the depreciation of dysfunction. So see, even you did about would be as it is, bless Here we'll use the productive able to find a depreciation of dysfunction. So see two times t it about d plus C two times heated about. Now we'll calculate you double prime tea. So it will big worlds too. Si won it about the as it is Bless again will use air productive to find an appreciation of dysfunction. So see too Damn Steve, you devoured d bless C two. It's about be on. The deflation of this function would be the same that they see to You did about over again, right this thing as two times off, See to everybody on Arab result. So it's one of the same thing. So we have calculator you prime three immutable. Probably not going to put the values in this equation differential equation. So you double prime tea is this? So we get, see even either power t bless C two times d unit of our be plus two times see to eat about. Is it quits too? Two games, you prime t. That means this one to see even a bit about the blessed see two times t it about be bless. See to you truth of our team minus you often. So you off days this but I'll write you off D as it is. Certificate observed carefully We can say that these two domes is equals to you often so begin right you off d blessed two times, see toe u to the power T is the calls to two times. See, even he'd unit of our tea bliss see to air times t eat about me. I'm taking this one in brackets and I'm separating this. Ah, no, Mr Moat. So two times C two it is about the minus You off If you observe carefully, these students represents you off b So the question becomes you off d plus two times see toe the body as equals to two times you off t plus two times See to it about the minus UFT. So here, this is two days and this is one time. Certainly I left with new times. Are you often So you can say that you off b plus two times See toe it about 30 and the girls to you off t plus two times. See, Do you live rt Hence we observed at the left side of the equation is equals to the right side so we can conclude Oregon very over again. See that the given function is the solution off the given differential equation.

Here. We have to verify that the given function right off B is it called to City Cube? Is the solution off the given differential equation which is de vie Prime D minus three Right off is equals to zero. Where C is hair see is constant so we can write this differential equation as de vie Prime d is equals toe three times. Why often have you ever calculated via prime tea? Why prime tea would be equal to the differentiation of this. So it will be three ct square when depart the values here. So we'll get tee times. Here it is. Three c d square. Is it closed with three times? Right off T or we can write this left side of the equation as three I'm taking outside and C B Cube is equals 23 Why off the If you observe carefully, we can say that this stone is equal to y awfully. It becomes three ryo. Fti recalls 23 Why often hence we have proof, Darda. The left side is equal right side. So we're very fired that the given function is the solution of the differential equation. I hope you got a problem. Thank you.

Something. Well, let's take our first derivative. If I've seen into the nebula five T plus five C, that's fine. See into the negative. Well, these definitely cancel each other on our end up zero, so they satisfy the differential efficient.


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