Question

Match each of the following differential equations with a solution from the list below. 1. y'' - 9y' + 18y = 0 2. 2x^2y'' + 3xy' = y 3. y'' + 9y' + 18y = 0 4. y'' + y = 0 A. y = cos(x) B. y = 1/x C. y = e^{-3x} D. y = e^{6x}

          Match each of the following differential equations with a solution from the list below.

1. y'' - 9y' + 18y = 0
2. 2x^2y'' + 3xy' = y
3. y'' + 9y' + 18y = 0
4. y'' + y = 0

A. y = cos(x)
B. y = 1/x
C. y = e^{-3x}
D. y = e^{6x}

Added by William G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Linda Hand

Step 1

y' - 9y + 18y = 0 This equation simplifies to y' + 9y = 0. This is a first-order linear homogeneous differential equation. The general solution for this type of equation is y = Ce^(-9x), where C is an arbitrary constant. So, the solution for equation 1 is D.y = Show more…

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Match each of the following differential equations with a solution from the list below. 1. y'' - 9y' + 18y = 0 2. 2x^2y'' + 3xy' = y 3. y'' + 9y' + 18y = 0 4. y'' + y = 0 A. y = cos(x) B. y = 1/x C. y = e^{-3x} D. y = e^{6x}