The discussion focuses on solving the second-order ordinary differential equation (ODE) represented as Y'' - (Y')² + (C1 * exp(Y)) = C2, where C1 and C2 are constants. The user attempts to derive a solution by substituting Y' with A and expressing Y as At + C3. The equation is then transformed into A' - (A²) + C1 * exp(C3) * exp(At) - C2 = 0, leading to A' - (A²) + C * exp(At) = 0 after simplification. The use of Wolfram Alpha for solving the ODE is also suggested as a resource.
PREREQUISITESThis discussion is beneficial for mathematics students, educators, and anyone involved in solving differential equations, particularly those seeking to understand second-order ODEs and their applications in various fields.
Please post your HW threads in the proper HW forum by subject. If you're not sure where they should go, you can always ask a Mentor for help.physicsguy43 said:Homework Statement
Y''-((Y')^2)+(C1*exp(Y))=C2
C1 and C2 are constants.
exp = e
Homework Equations
No clue how to start this
The Attempt at a Solution
Y'=A=dY/dt
Y=At+C3 (not sure)
A'-(A^2)+C1exp(At+C3)-C2=0
A'-(A^2)+C1exp(C3)exp(At)=0
let C=C1*exp(C3)
A'-(A^2)+Cexp(At)=0
Right, that helps me a lot, thanks!Dr. Courtney said: