Question

A homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given below. 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. y'' - 6y' = 0; y1 = 1, y2 = e^{6x}; y(0) = 2, y'(0) = -1. y(x) =

          A homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given below. 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.
y'' - 6y' = 0; y1 = 1, y2 = e^{6x}; y(0) = 2, y'(0) = -1.
y(x) =

A homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given below. 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.
y” - 6y' = 0; y1 = 1, y2 = e^6x; y(0) = 2, y'(0) = -1.
y(x) =

Added by Dave D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Suchitra K

04/06/2022

Step 1

For \(y_2 = 9e^{6x}\): \(y_2'' = 36e^{6x}\) and \(y_2' = 6e^{6x}\) Substitute into the differential equation: \(36e^{6x} - 6(6e^{6x}) = 0\) Therefore, \(y_2\) is also a solution of the differential equation. ** Show more…

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A homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given below. 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. y'' - 6y' = 0; y1 = 1, y2 = e^6x; y(0) = 2, y'(0) = -1. y(x) =