Question

Of the following, which is not a solution to the differential equation y′′′+4y′=0?

A. Y=10


B. Y=4e⁻²ˣ


C. Y=3sin(2x)


D. Y=2cos(2x)+4

Answer 1

To determine which of the given options is not a solution to the differential equation y′′′+4y′=0, we substitute each option into the equation and check for the satisfaction of the equation. Option B, y = 4e⁻²ˣ, does not satisfy the equation.

Step-by-step explanation:

To determine which of the given options is not a solution to the differential equation y′′′+4y′=0, we need to substitute each option into the equation and check if it satisfies the equation. Let's substitute each option into the equation:

A. y = 10: Differentiating three times, we get y′′′ = 0, and 4y′ = 0×10 = 0. Therefore, the equation is satisfied.

B. y = 4e⁻²ˣ: Differentiating three times, we get y′′′ = 0, and 4y′ = 4×(-2)e⁻²ˣ = -8e⁻²ˣ. Therefore, the equation is not satisfied.

C. y = 3sin(2x): Differentiating three times, we get y′′′ = 8sin(2x), and 4y′ = 4×(2)cos(2x) = 8cos(2x). Therefore, the equation is satisfied.

D. y = 2cos(2x)+4: Differentiating three times, we get y′′′ = -16cos(2x), and 4y′ = 4×(-2)sin(2x) = -8sin(2x). Therefore, the equation is satisfied.

From the above analysis, we conclude that option B, y = 4e⁻²ˣ, is not a solution to the differential equation y′′′+4y′=0.