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=e* cos x, y₂ = ex sin x; y(0) = 7, y'(0) = 19 Why is the function y₁=e* cos x a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice. OA. The function y₁ = ex cos x is a solution because when the function, its first derivative, y₁' = statement. OB. The function y₁ = ex cos x is a solution because when the function and its indefinite integral, and its second derivative, y₁"' = are substituted into the equation, the result is a true , are substituted into the equation, the result is a true statement.
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=e* cos x, y₂ = ex sin x; y(0) = 7, y'(0) = 19 Why is the function y₁=e* cos x a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice. OA. The function y₁ = ex cos x is a solution because when the function, its first derivative, y₁' = statement. OB. The function y₁ = ex cos x is a solution because when the function and its indefinite integral, and its second derivative, y₁"' = are substituted into the equation, the result is a true , are substituted into the equation, the result is a true statement.
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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Transcribed Image Text: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 = e* cos x, y₂ = e* sin x; y(0) = 7, y'(0) = 19
Why is the function y₁ = e* cos x a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice.
' =
OA. The function y₁ = e* cos x is a solution because when the function, its first derivative, y₁
statement.
B. The function y₁ = ex cos x is a solution because when the function and its indefinite integral,
and its second derivative, y₁ " = are substituted into the equation, the result is a true
"
are substituted into the equation, the result is a true statement.
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