Question

If \(a\) and \(b\) are arbitrary constants, then the differential equation representing the family of curves \[ y=a\sin(x+b) \] is

• A. \(\frac{d^2y}{dx^2}-y=0\)
• B. \(\frac{d^2y}{dx^2}+y=0\)
• C. \(\frac{d^2y}{dx^2}-y^2=0\)
• D. \(\frac{dy}{dx}-y=0\)

Hint:

For \(y=a\sin(x+b)\), differentiating twice gives the relation \(y''=-y\).

Answer 1

The Correct Option is B