Thread: [SOLVED] Second order differential equations

b)
Solve the initial value problem

y′′ + 2y′ + 5y = 0, y(0) = −2, y′(0) = 2

and write the final solution using real valued functions.

I did the question and got the answer to be Y = -2(e^x)cos2(x) is ithis right?

Help will be appreciated...thank you

Originally Posted by rajr

b)
Solve the initial value problem

y′′ + 2y′ + 5y = 0, y(0) = −2, y′(0) = 2

and write the final solution using real valued functions.

I did the question and got the answer to be Y = -2(e^x)cos2(x) is ithis right?

Help will be appreciated...thank you

So the auxillary equation is



this tells us that our solution is of the form



Your answer is correct except for the missing minus sign in you exponential