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Have an equation;
d2y(t)/dt2 + 5d2y(t)/dt2 + 4y(t) = 2e-2t
Solved the complementary(homogenous) part and the function and got the roots of -1 and -4
so the yh(t) is A1.e-4t + A2.e-t
Forcing function is 2.e-2t so yparticular(t) is A.e-2t
Am I right here ? Or am I supposed to use Ate-2t
Well, if I use the first one, the resultant function doesn't give me the 2.e-2t when I put it into the differential equation, so there is something wrong obviously.
However F(t) or one of its derivatives are not identical to terms in the homogenous solution, so I think I have to use the first option, which is A.e-2t
After proceeding I ended up with yp(t) = 1/3.e-2t
Initial values are y(0) = 0 and y(1)(0) = 0
so, K1 = -1/9 and K2 = -2/9
Still couldn't find where I am wrong
Appreciate if you help me.
d2y(t)/dt2 + 5d2y(t)/dt2 + 4y(t) = 2e-2t
Solved the complementary(homogenous) part and the function and got the roots of -1 and -4
so the yh(t) is A1.e-4t + A2.e-t
Forcing function is 2.e-2t so yparticular(t) is A.e-2t
Am I right here ? Or am I supposed to use Ate-2t
Well, if I use the first one, the resultant function doesn't give me the 2.e-2t when I put it into the differential equation, so there is something wrong obviously.
However F(t) or one of its derivatives are not identical to terms in the homogenous solution, so I think I have to use the first option, which is A.e-2t
After proceeding I ended up with yp(t) = 1/3.e-2t
Initial values are y(0) = 0 and y(1)(0) = 0
so, K1 = -1/9 and K2 = -2/9
Still couldn't find where I am wrong
Appreciate if you help me.