- #1
PeteSampras
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Homework Statement
I need to solve the follwing differential equation
$$(\frac{df}{dt}) \dfrac{4 n e^{4nf(t)}-9n e^{2nf(t)} (\frac{df}{dt})^2 + e^{2nf(t)} r^2 \frac{d^2f}{dt^2}+5n (\frac{df}{dt})^4 r^4 - r^4 \frac{d^2f}{dt^2} (\frac{df}{dt})^2}{-e^{2nf(t)}+ (\frac{df}{dt})^2 r^2}=0 $$
Homework Equations
r,n are constants >0
The Attempt at a Solution
I tried to solve in Maple the factor
$$4 n e^{4nf(t)}-9n e^{2nf(t)} (\frac{df}{dt})^2 + e^{2nf(t)} r^2 \frac{d^2f}{dt^2}+5n (\frac{df}{dt})^4 r^4 - r^4 \frac{d^2f}{dt^2}(\frac{df}{dt})^2=0$$
but the only solution that i find is such that the denominator is 0.
Also i think in a assumption ##\frac{df}{dt} \approx \epsilon## with ##\epsilon^3 \approx 0## but this is a solution of the form ##f(t) = \ln ( g(t) ) ## , ¿but the derivative is not small?
Help please
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