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EXERCISES 4.3In Problems 1~14 find the general solution of the given second-order diflerential equation. 1, 4y" +y =0 2. 36y 3.Y Ey 6y = 0 4. y' 3y' ...

Question

EXERCISES 4.3In Problems 1~14 find the general solution of the given second-order diflerential equation. 1, 4y" +y =0 2. 36y 3.Y Ey 6y = 0 4. y' 3y' + 2y = 0 5.y" + 8y' + I6y = 0 6. y IOy + 2Sy7.12y" Sy'Zy = 08. y" + 4y9.y" + 9y = 010. 3v11. }"4y' + Sy = 012. 2y' + 2y T y13. 3y" + 2y' +y = 014.-2y" Jy' + 4

EXERCISES 4.3 In Problems 1~14 find the general solution of the given second-order diflerential equation. 1, 4y" +y =0 2. 36y 3.Y Ey 6y = 0 4. y' 3y' + 2y = 0 5.y" + 8y' + I6y = 0 6. y IOy + 2Sy 7.12y" Sy' Zy = 0 8. y" + 4y 9.y" + 9y = 0 10. 3v 11. }" 4y' + Sy = 0 12. 2y' + 2y T y 13. 3y" + 2y' +y = 0 14.-2y" Jy' + 4



Answers

In Exercises $1-30,$ find the general solution of the given equation.
$$4 y^{\prime \prime}-4 y^{\prime}+13 y=0$$

Solutions. We have to find a general solution for this. Given differential equations. First we will write the equation for this has given differential equation. That is out of the power four plus four. Our people are six R squared plus four are Plus one. It costs 20. Okay so we will simplify it so we can write it our plus one to the power of four. That is close to zero. So the rules of this angry question baby one is one going one is 11. This one one as well. So general solution will be general solution. Can witness what it costs to seven Plus C2 T plus the three. The script let's say for take you Into into the power of -1 into T. So this can witness seven Plus sea duty. Let's see through the square. Let's see four. Mhm. Into the to the power of Manistee. So this is the general solution of this given differential equations. I hope you understood. Thank you.

In discussion will even know one type of Graham pressed for white cramp. Plus, my wife coaches zero in the first images of the characteristic a question where we're all square thus far, plus nine vehicle to their oh, and using the phonetic formula again. I want todo coaching when this paper's gonna square b squared C to any so we can include it among a strong person minus 16 miners. This one will be four times. I will be 36 evading. But you think so? Getting whatever minus four plus minus squared on the minus 20 over. True. Then we can register into the minus four. Plus the miners doesn't obey that Joe squared under five. I want what you are going to understand. You know, minus June President might have scuttled in the fight. I So from here we can find a generous lotion. Why would a coach in the C one Agent Ministry t ghosts I screamed my thing plus cto et Manus treaty signed scheduled for 5 30

Hello. We have to find a general solution for this. Given the translate questions. So first we'll write the obviously question for this that is our to the powerful plus two R. Squared. There's many questions Jerusalem the so this is our scope has one to the power of to that is equal to zero. Our school president into this couples advantages cost €2 a premier or will because to plus minus iota four plus minus older. So general solution can witness general solution. Can we witnessed what it costs to Stephen Plus C2 states. General solution can be will be coastal into the power of zero in 2 weeks during duty To see even plus C2 P of costing Plus the three plus C four D off costea. So why will be questioned? seven plus you too. Do you have cost you plus C. Three plus C 40 of scientific. This is the general solution. So this is the answer. I hope you understood. Thank you.

Hello. We have to find a general solution for this given differential equation. That is we can add the three of viable. The excuse -4 due to value upon DX Square Plus three and 2. Dave I upon dx That is costing zero. So we will denote the upon Diaz that is by device So we can write due to the power three or five minutes for the square Plus three day into white It cost 20. So from here we can Right so we can decide the q minus for the square. That's really this is the auxiliary equation for this given differential equation. Auxiliary equation showdown. No that factor of this actually occasion will be The into the Square -40 plus D. That is close to zero. That is the Here this Baby three. So this is d minus. Wanting to D -330 request to Jerusalem the root of this order execution group of this factor Route of the soldier in question will be zero one and 3. So general solution can written us. So general solution will be Why cause to seven You do the power zero x plus ito into the power of one and two years plus C. Three to the power three X. So this is the cost of white. Close to seven plus C. Two to the power X plus C. Three U. To the power of three X. So this is the general solution of this given differential equation. I hope you understood. Thank you


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