Question

Write out Theorem 1 specifically for the cases n=1 and n=2

Answer 1

The original Theorem 1 states that If Po, P1,...,Pn-1, q are continuous on (a,b) and Xo is any number in the interval (a,b) and yo,y'o,...,y^(n-1)o are any numbers then there is a unique function y which is a solution of Y^(n)+Pn-1(x)y^(n-1)+...+p1(x)y'+po(x)y=q(x)
such that y(Xo)=Yo, y'(Xo)=y'o,...,y^(n-1)(Xo)=y^(n-1)o

Answer 2

hmm how am I supposed to write the same theorem from n=1 and n =2, plug n in? x.x

Answer 3

anyway redrawn version...
The original theorem 1 states that if

are continuous on (a,b) and
is a number in the interval (a,b) and are any numbers then there is a unique function y which is a solution of
such that