# Thread: Differentiating y= Acosαx + Bsinαx and finding Constants

1. ## Differentiating y= Acosαx + Bsinαx and finding Constants

Don't really know what to do with this one, any help welcome

If A, B and α are constants, independent of x, and

y= Acos
αx + Bsinαx

Evaluate the derivates
y'=dy/dx
y^n=d^2y/dx^2

Determine values of A, B and α such that y satisfies
y^n+y=0 and y(0)=0, y'(0)=1

I've tried to differentiate y
y'=
-αAsinαx + αBcosαx
y'=αBcosαx - αAsinαx

y^n=
αBsinαx + ααAcosαx
y^n=ααAcosαx - ααBsinαx

2. Originally Posted by zombieguy
Don't really know what to do with this one, any help welcome

If A, B and α are constants, independent of x, and

y= Acosαx + Bsinαx

Evaluate the derivates
y'=dy/dx
y^n=d^2y/dx^2

Determine values of A, B and α such that y satisfies
y^n+y=0 and y(0)=0, y'(0)=1

I've tried to differentiate y
y'=-αAsinαx + αBcosαx
y'=αBcosαx - αAsinαx

y^n=αBsinαx + ααAcosαx
y^n=ααAcosαx - ααBsinαx
The expression $\displaystyle y^n=\frac{d^2y}{dx^2}$ doesn't really make any sense to me. Is $\displaystyle y^n$ supposed to be the nth derivative? Equal to the 2nd derivative?

3. $\displaystyle y^n$ is equal to the 2nd derivate