A homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of the differential equation. Then find a particular solution of the form y=c1y1+c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x.y′′−2y′+2y=0; y1=excosx, y2=exsinx; y(0)=12, y′(0)=11Why is the function y1=excosx a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice. Why is the function y, = eX cos x 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, = eX cos x 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 statemenO B. The function y, = eX cos x 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, = eX sin x 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, = eX sin x is a solution because when the function, its first derivative, y,' =and its second derivative, y2"=are substituted into the equation, the result is a true statement.O B. The function va = ex sin x is a solution because when the function and its indefinite integral,are substituted into the equation, the result is a true statement.The particular solution of the form y =c,y, + Czy2 that satisfies the initial conditions y(0) = 12 and y' (0) = 11 is y =.

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Answered: A homogeneous second-order linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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A homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of the differential equation. Then find a particular solution of the form y=c1y1+c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x. y′′−2y′+2y=0; y1=excosx, y2=exsinx; y(0)=12, y′(0)=11 Why is the function y1=excosx a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice.

Why is the function y, = eX cos x 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, = eX cos x 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 statemen
O B. The function y, = eX cos x 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, = eX sin x 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, = eX sin x is a solution because when the function, its first derivative, y,' =
and its second derivative, y2"=
are substituted into the equation, the result is a true statement.
O B. The function va = ex sin x is a solution because when the function and its indefinite integral,
are substituted into the equation, the result is a true statement.
The particular solution of the form y =c,y, + Czy2 that satisfies the initial conditions y(0) = 12 and y' (0) = 11 is y =.

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