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Find the general solution to the equation:2y( 4) = ]y +( tant)y =cos?t,...

Question

Find the general solution to the equation:2y( 4) = ]y +( tant)y =cos?t,

Find the general solution to the equation: 2 y( 4) = ] y +( tant)y =cos?t,



Answers

Find the general solution of the following equations. $$y^{\prime}(x)+2 y=-4$$

All right, Silver problem. Seven. We have to find the general solution to this differential equation. And the first so we're gonna isolate the white crime. So we're gonna so tracked both size by two. Why? And those were gonna get why? Primacy goes and negative to line lines for on the right side, we're gonna factor other negative to simplify it. So it's giving negative two times. Why Post for and on the left side, we're going to rewrite the White Prima's d Y over DX, and we're gonna set them equal to each other. And we have to get all the wise on one side on all the exits on the other side. So we're gonna want to fly both sides by D X and we're gonna end up with the wise. You go toe negative two times y plus two all times, DX. And then we divide both sides by y plus two. So it's gonna be won over WIPO's to you. Why Singleton get to 50 X and then we integrate with science. So we're gonna get Ellen on why? Plus two, it's for that thing to expose seat, and you just don't need the one constant in person is. Both sides will end up with the constant number Bacon. Subtract one from the other. So now we have to get rid of this. Ellen. So we started asking exponents of you, and we do it for both sides. So, Ellen, then you're gonna castle house, organ. And that was why close to it to go that you need to learn together to express seat. You subtract two from both sides and we're gonna get why secrets that you to the power of negative two x plus steam likes to. And the thing about wasn't you to the negative two x plus e is that is equal to each the negative two x times each of the power seat. Well, the things that years a constant number. So when you raise it to a constant exponents, it just becomes another constant number. So in the end, we're actually going to have lies either the sea time you to them. Negative. Two X minus two. Yeah. This is basically else

Great. You did your part. Bars were you hear? Square, same square. Kill you.

In this question we have to find the solution of the linear differential equation. That is why the sharks equals 2 -2 by -4. So we know that if I die differential equation it's Wild dash access. It was to Okay why? Let's be then we can say that the solution of the differential equation if it was too Why is it was to see it is to be powered K. X And -7. Like a. So do delicious written if we compare the differential equation with this given differential equation And then K is -2 here And B is -4. So due to this reason, I can say that now the solution must be while it was to see Areas to the Power -2, works -7 is -4 And Divide by KC -2. After simplifying it we can see it. We get by request to see areas to the power -2 weeks minus two. So this is the required solution of the given differential equation. And here we can see that C. Is any constant. Okay thank you.

Wide of time kind. You hear? Why? Carol's e card? You know first.


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