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Numerade Educator



Problem 6 Easy Difficulty

Use power series to solve the differential equation.

$ y'' = y $


$y=a \cdot e^{x}+b \cdot e^{-x}$


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Video Transcript

today we're going to solve problem number six. Yes, in the solution is for the form by Dickens Sigma in equal to zero to infinity. See and access to it. Why're icicles Sigma and negative one to infinity N. C and exist in minus more rideable icicles, sigma and nickel toe to in 50 and in due and minus one into C and access to end minus two. We had to solve by double icicles white. So sigma any go toe to toe and 50 and in two in minus one. See an access and minus two equals sigma in equal to zero to infinity, See and express Do it so did not in equal to zero to infinity and plus to indu and plus one into seeing plus two express to n equals sigma and equal zero pain. 20. Seeing access to it. We can write Sigma and equal to zero to infinity and plus two into and press one in to see in close to minus C and access to And because zero all the songs toe the zero we have and plus two and plus one See and plus to minus C and equal to zero See and just do it because, see and diverted by and plus one in tow and plus two C two equals sees the road divided by zero plus one into zero plus two, which is C zero by one in tow. Okay, then C four equals C two developed by toe plus one in do two plus two, which is sees the road developed by 1 92 then three into full C six equals You get like sees already wanted by one into two. Three into four. 506. So see to any calls. She is road divided by two in factorial. Then we have C three because, see, when they were at bite one plus one in the one plus two it is he's already were bike doing the tree See for me because see through the or everybody three plus one in the three plus two It physical to see when they were hit by doing the three in the four in the fight, C six equals, so receives haven't equals C zero developed by two in three foreign to fight in the 16 to 7, so c two and plus one equals C one divided by do n plus one factorial so we can write like by equals Sigma and Nico 2010. 50 See and access to and which is a go to sigma in negative zero to infinity. See off doing access to toe, plus a negative 0 10. 50. See off to in person one excessive twin plus one, which is a kowtow stigma in equal to zero to infinity. Si no existed to and developed by two in factory Plus they let me go to 0 10 50. See you one excited to win Plus one developed by to any plus one for total for which is like 60 in tow. Sigma and equal to zero to infinity existed to and directed by two in factorial, plus the one into sigma, and they go to zero to infinity, it says to two and plus one different by two and plus one factory we will get like sees little. It escalates, plus the rest of minus X plus C one. It restricts minus arrest of minus six, which is a photo he restricts in the C zero plus C one plus arrested minus six c zero minus c work. So which is ableto Hindu. It restricts plus B in tow. It is two minus sets. That's the end off a question. Thank you.