Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .
In the question ,
it is given that ,
the differential equation is
y'' + 9y + 5y³ = Cos(10t) ...equation(1)
y(0) = 0, y'(0) = 1
for y = 0 , the differential equation is
y''(0) + 9y(0) + 5{y(0)}³ = Cos90)
y''(0) + 9 + 5 = 1 ;
y''(0) = 1.
differentiating equation(1) with respect to "t" , we have
y''' + 9y' + 15y²y' = -10Sin(10t)
y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)
y'''(0) + 9 + 0 = 0
y'''(0) = -9
The Taylor series is given by
y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....
Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have
y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....
= t + t²/2 - 3/2.t³ + ...
Therefore , the first three terms are t , t²/2 , -3/2.t³ .
Learn more about Taylor Series here
https://brainly.com/question/13163878
#SPJ4
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
