Consider the nonhomogeneous differential
equationy"-2y'-3y=2(e^(
find a paricular solution to the non homogeneous equation.
also write the general solutiong to the
nonhomogeneousequation.

Step-by-step explanation:

For homogeneous solution:

So since roots are r = 3 and r = -1,

Since we are given , we will use undetermined coefficients. However, here the trick is we have in homogeneous solution. So in particular solution, as undetermined coefficients, we will use instead of .

Hence,

So,

Hence,

General solution is:

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.

step-by-step explanation: