Question

how to solve the following ODE?

Answer 1

@mukushla help !!!!!!!!!!!!!!!

Answer 2

Book says this can be changed into
Riccati equation . How ????

Answer 3

then ? why are you using two change of variables ?
never did this before using the first change of variables y=e^z i am getting
\[\Large (z''+(z')^2)e^{2z}+(z'e^z)^2-(e^z)^2=0\]
how to move from here?

Answer 4

divide by \(e^{2z}\)

Answer 5

ok

Answer 6

\[\Large z''+(z')^2+(z')^2-1=0\]
\[\Huge z''+2(z')^2-1=0\]

Answer 7

now?

Answer 8

now let \(z'=p\)

Answer 9

p'+2p^2-1=0

Answer 10

yeah....so \(p'=1-2p^2\)

Answer 11

is this a riccati?

Answer 12

yes !!!!!!
because general form is .

Answer 13

thanks man you saved my life :P

Answer 14

np man..:)