Question

How do I solve the differential equation: f''(x)=-f(x) with f(0)=12 and f'(0)=-7?

Answer 1

Note that this is a second order linear ODE. For this kind of differential equation which we can re-arrange to be \(\bf y''+y=0\), the solution will exist in the form \(\bf f(x)=c_1sin(x)+c_2cos(x)\). Use the given information that \(\bf f(0)=12\) and \(\bf f'(0)=-7\) to figure out the values of \(\bf c_1\) and \(\bf c_2\).

@slayereyals