Determine a particular solution for the subsequent differential equation.

y′′ - 4 y′ -12 y = 3e5t + sin(2t) + te4t

Solution

This example is the purpose that we've been using similar homogeneous differential equation for all the previous illustrations. There is nothing to do along with this problem.  All that we require to do it go back to the appropriate illustrations above and find the particular solution from that illustration and add them all together.

Doing this provides,

Y_P(t) = - (3/7) e^5t + (1/40) cos(2t) - (1/20) sin(2t) - (1/36) e^4t