Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y
by differentiating the second equation with respect to t and substituting for x from the first equation. Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0)=4 and y(0)=5, what are x and y?