Question

Find a formula for the solution of the initial value problem $y'' + 25y = f(t)$, $y(0) = 3$, $y'(0) = -8$. y(t) = + \int_0^t

          Find a formula for the solution of the initial value problem $y'' + 25y = f(t)$, $y(0) = 3$, $y'(0) = -8$.
y(t) = 
+ \int_0^t

Find a formula for the solution of the initial value problem y” + 25y = f(t), y(0) = 3, y'(0) = -8.
y(t) =
+ ∫0^t

Added by Nieves M.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Owen Jacobs

09/12/2021

Step 1

This is a second-order linear differential equation with constant coefficients. The characteristic equation is r^2 + 25 = 0, which has complex roots r = ±5i. Therefore, the general solution to the homogeneous equation is: y_h(t) = C1 * cos(5t) + C2 * sin(5t) Show more…

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Find a formula for the solution of the initial value problem y^('')+25y=f(t),y(0)=3,y^(')(0)=-8. y(t)= +int_0 Find a formula for the solution of the initial value problemy+25y= f(t),y0)=3,y'0)=-8 y(t)= dT