Consider the first order ODE for the function

y=y(x)

:\

y^(')=cosh(y)

\ Solve for a 1-parameter family of solution with some parameter

C

.\ (You may need to do a substitution, as a hint:

u=e^(x)

could help, and remember a fun function.)\ If you do it correctly, this 1-parameter family of solution should be expressible in a nice form

y(x)=F(G((x)/(2)+C))

, for some familiar transcendental function

F

and

G

.\ The usual symbol for

F

is and for

G

is\ P.S. Actually, this family of function can also be expressed as

F(G(x+C))

, for some different

F

, but I think that's harder. But if you figured out how to do both ways, I will give you some stickers in class!

Consider the first order ODE for the function y=y(x) : y=cosh(y) Solve for a 1-parameter family of solution with some parameter C. (You may need to do a substitution, as a hint: u=ex could help, and remember a fun function.) If you do it correctly, this 1-parameter family of solution should be expressible in a nice form y(x)=F(G(2x+C)), for some familiar transcendental function F and G. The usual symbol for F is and for G is P.S. Actually, this family of function can also be expressed as F(G(x+C)), for some different F, but I think that's harder. But if you figured out how to do both ways, I will give you some stickers in class