Question

What is the value of \[\frac{d^{2}y}{dx^{2}}+y\] for \[y=a\sin(x+b)\]?

Options

• \[a\sin(x+b)+a\sin(x+b)=2a\sin(x+b)\]

• \[a\cos(x+b)+a\sin(x+b)=0\]

• \[-a\sin(x+b)+a\sin(x+b)=0\]

• \[-a\cos(x+b)+a\sin(x+b)=0\]

Answer 1

For this function, \[\frac{d^{2}y}{dx^{2}}=-a\sin(x+b)\] and \[y=a\sin(x+b)\]. Their sum is zero, so the differential equation is satisfied.