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Numerade Educator

# Use power series to solve the differential equation.$y' - y = 0$

## $$c_{0} \sum_{n=0}^{\infty} \frac{x^{n}}{n !}=c_{0} e^{x}$$

#### Topics

Second-Order Differential Equations

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### Video Transcript

today we're going to solve a problem above here. Y dash minus y equals zero. Use my equals. Sigma n equals zero to infinity Seeing extent, it says to sort of So why does equals Sigma n equals one to infinity Seeing star and star access to end minus one by allies equals sigma and equal zero to infinity see and plus one star and plus one express to it Food sigma in equal to zero to infinity See and plus one start and plus one express doing minus sigma a nickel toe one for n equals zero to infinity See and express to n equals zero. So Cigna an equal to zero to infinity seat and plus one and plus one minus c and start express to him for n equals zero See when he calls See, not foreign equals one Steve too. Because half see not which is ego zero. And he goes to C three because one by three star one by to see nautical zero Seeing it was one by in factorial feel Why equal to see you? Yeah, Sigma en equal to zero to infinity. One way in factorial extra student. So light equals C zero are here in states. That's the end off a question. Thank you

University of New Mexico

#### Topics

Second-Order Differential Equations

Lectures

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