Super lost right now. please help. A homogeneous second-order linear differential equation, two functions y, and y,, and a pair of initial conditions are given. First verify that y, and y, are solutions of the differential equation. Then find a particular solution of the formy = cy, +Cy, that satisfies the given initial conditions. Primes denote derivatives with respect to x.y" +2y' +y 0; y1 = e =X,-X.Y2 =Xe¯^, y(0)= 9, y'(0) = – 7Why is the function y, = ea solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice.O A. The function y, = e is a solution because when the function, its first derivative y,and its second derivative, y,are substituted into the equation, the result is a true statement%DO B. The function y, = e is a solution because when the function and its indefinite integral,are substituted into the equation, the result is a true statement.Why is the function y2 =x ea solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice.O A. The function y, =x eX is a solution because when the function and its indefinite integral,are substituted into the equation, the result is a true statement.and its second derivative y,are substituted into the equation, the result is a true statement.O B. The function y, =xe is a solution because when the function, its derivative, y,The particular solution of the form y = c, y, + C, y, that satisfies the initial conditions y(0) = 9 and y'(0) =-7 is y=.?Click to select your answer(s).

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Description: Super lost right now. please help. A homogeneous second-order linear differential equation, two functions y, and y,, and a pair of initial conditions are given. First verify that y, and y, are solutions of the differential equation. Then find a part

By putting the function in the differential equation find that the this function satisfies the…

A homogeneous second-order linear differential equation, two functions y, and y,, and a pair of initial conditions are given. First verify that y, and y, are solutions of the differential equation Then find a particular solution of the form = Cy, +Czy2 that satisfies the given initial conditions. Primes denote derivatives with respect to x y" +2y' +y = 0: y1 = e, y2 =xe * y(0) = 9, y'(0) = - 7 Why is the function y, = e a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice O A. The function y, = e -X is a solution because when the function, its first derivative y,'= and its second derivative, v."= are substituted into the equation, the result is a true statement O B. The function y, = ex is a solution because when the function and its indefinite integral are substituted into the equation, the result is a true statement Why is the function y, =xe -X a solution to the differential equation? Select the correct choice below and fill in the answer box to complete vour choice O A. The function y, =xe -X is a solution because when the function and its indefinite integral are substituted into the equation, the result is a true statement O B. The function y, =xe -X is a solution because when the function, its derivative y,= and its second derivative y,'= are substituted into the equation, the result is a true statement The particular solution of the form y = c, y, + c,y2 that satisfies the initial conditions y(0) = 9 and y'(0) = - 7 is y= Click to select your answer(s).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Super lost right now. please help.

A homogeneous second-order linear differential equation, two functions y, and y,, and a pair of initial conditions are given. First verify that y, and y, are solutions of the differential equation. Then find a particular solution of the form
y = cy, +Cy, that satisfies the given initial conditions. Primes denote derivatives with respect to x.
y" +2y' +y 0; y1 = e =X,
-X.
Y2 =Xe¯^, y(0)= 9, y'(0) = – 7
Why is the function y, = e
a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice.
O A. The function y, = e is a solution because when the function, its first derivative y,
and its second derivative, y,
are substituted into the equation, the result is a true statement
%D
O B. The function y, = e is a solution because when the function and its indefinite integral,
are substituted into the equation, the result is a true statement.
Why is the function y2 =x e
a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice.
O A. The function y, =x e
X is a solution because when the function and its indefinite integral,
are substituted into the equation, the result is a true statement.
and its second derivative y,
are substituted into the equation, the result is a true statement.
O B. The function y, =xe is a solution because when the function, its derivative, y,
The particular solution of the form y = c, y, + C, y, that satisfies the initial conditions y(0) = 9 and y'(0) =-7 is y=.
?
Click to select your answer(s).

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