Second order differential equation?

Question

y" + 2y' + 2y = 0
y(1) = 1, y'(1) = 2

Okay... i was able to find the general solution to this problem, but since the initial values are given at 1 (which involves taking the values of sin1 and cos1....) i couldn't solve for the constant coefficients. Can anyone help?

Answer 1

instead of expressing the solution in sin and cosine, you can express the solution in terms of exponential.....this way, you can apply the initial conditions

the general solution for this ODE is
y=(c1)e^(1+i)x + (c2)e^(1-i)x

apply the initial conditions to solve for C1 and C2

Answer 2

What is the problem with sin(1) and cos(1)? There are no limits on the arguments to sin and cos. The arguments are in radians, so sin(1) = 0.8415 and cos(1) = 0.5030. 1 (radian) = 57.2958º