We want to find functions p(t), q(t), f(t) such that(a) p and q are continuous functions on the open interval (0,π).
(b) f is an infinitely differentiable nonzero function on the whole real line (−∞,∞) such that f(0)=f′(0)=f′′(0).
(c) y=sint and y=f(t) are solutions of the differential equation y′′+p(t)y′+q(t)y=0 on (0,π).Is this possible? Either prove this is not possible, or show this is possible by providing an explicit example of such f,p,q. differential equationscalculus