Question

Problem 3. Solve the homogeneous differential equation d^2y/dx^2 + 2 dy/dx - 24y = 0, and the related, nonhomogeneous differential equation d^2y/dx^2 + 2 dy/dx - 24y = 16 - (x + 2)e^{4x}.

          Problem 3. Solve the homogeneous differential equation

d^2y/dx^2 + 2 dy/dx - 24y = 0,

and the related, nonhomogeneous differential equation

d^2y/dx^2 + 2 dy/dx - 24y = 16 - (x + 2)e^{4x}.

Added by George B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

07/31/2023

Step 1

Substituting this into the differential equation, we get: m^2e^(mx) + 2me^(mx) - 24e^(mx) = 0 Dividing both sides by e^(mx), we get: m^2 + 2m - 24 = 0 Solving for m, we get: m = -6 or m = 4 Therefore, the general solution to the homogeneous differential Show more…

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Problem 3. Solve the homogeneous differential equation d^2y/dx^2 + 2dy/dx - 24y = 0 and the related, nonhomogeneous differential equation d^2y/dx^2 + 2dy/dx - 24y = 16 - (x + 2)e^(4x).