Originally Posted by
TshingY i need help on how to solve this differential equation
y'' = y' * e^y
initial conditions
y(0) = 0
y'(0) = 2
first i use u = y' and y'' = u*du/dy substitution to get
u*du/dy = u * e^y ---> du/dy = e^y
separating variables and integrating both sides give
u = e^y + c1 (*)
substituting y' back into u and separating variables give
dy / (e^y + c1) = dx
integrating gives
[ln(e^y) - ln(e^y + c1)] / c1 = x + c2
y - ln(e^y + c1) = c1*(x + c2) (**)
from here i am stuck. I can't get it to be in the form of y =