Purchase Solution

Homogeneous, Particular, and General Solutions

Not what you're looking for?

Ask Custom Question

Y''(t) + 6y'(t) + 13y(t) = te^(-t)
Compute the homogeneous solution yh(t).
Compute the particular solution yp(t).
Compute the general solution y(t) if y(0)=0 and y'(0)=1/8

Purchase this Solution

Solution Summary

The solution explains clearly and concisely the calculations necessary to reach the homogeneous, particular and general solutions of the given equation.

Solution Preview

Homogeneous Solution:

Aux. equation is: m^2 + 6m +13 = 0
m = (1/2)[-6 (+/-) sqrt(36-52) = -3 (+/-) i2

Two complex roots, m1 = -3+i2 and m2 = -3-i2

Hence, the homo. solution is:

yh(t) = e^(-3t) * [C1*Cos 2t + C2*Sin 2t]

Particular Solution:

Forcing function = te^(-t)
So, solution should ...

Purchase this Solution

Free BrainMass Quizzes
Architectural History

This quiz is intended to test the basics of History of Architecture- foundation for all architectural courses.