Question

Why is \[y=a\sin(x+b)\] a general solution of \[\frac{d^{2}y}{dx^{2}}+y=0\]?

Options

• It contains no arbitrary constants and gives a single number

• It is obtained by assigning fixed values to \[a\] and \[b\]

• It satisfies the differential equation and contains two arbitrary constants \[a\] and \[b\], equal to the order of the differential equation

• It satisfies the differential equation and contains one arbitrary constant, equal to the order

Answer 1

The equation \[\frac{d^{2}y}{dx^{2}}+y=0\] is of order two. The solution \[y=a\sin(x+b)\] contains the two arbitrary constants \[a\] and \[b\] and satisfies the equation.