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Consider the differential equation (DE): (y(15))² + 7t²e²ty(11) + y" = 106t³ + y − 3ty' a) Its order is b) Its degree is c) Generally, for a DE whose order is two more than the order of the one given above, how many initial conditions are needed to find a particular solution?

Consider the differential equation (DE): (y(15))² + 7t²e²ty(11) + y" = 106t³ + y − 3ty' a) Its order is b) Its degree is c) Generally, for a DE whose order is two more than the order of the one given above, how many initial conditions are needed to find a particular solution?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the differential equation (DE): (y(15))² + 7t²e²ty(11) + y" = 106t³ a) Its order is b) Its degree is +y-3ty' c) Generally, for a DE whose order is two more than the order of the one given above, how many initial conditions are needed to find a particular solution?
Transcribed Image Text:Consider the differential equation (DE): (y(15))² + 7t²e²ty(11) + y" = 106t³ a) Its order is b) Its degree is +y-3ty' c) Generally, for a DE whose order is two more than the order of the one given above, how many initial conditions are needed to find a particular solution?
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Step 1

Solution:

(y(15))2 + 7t2e2ty(11) + y'' = 106t^3 + y - 3ty'

=> (y(15))2 + 7t2e2ty(11) + y'' + 3ty' - y = 106t^3

 

 

(a) order of a DE is the highest order derivative appearing in the DE. 

    So, order of the DE is 15. [Ans]

(b) degree of a DE is the power to which the highest order derivative raised. 

   So, degree of the DE is 2. [Ans]

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