# Solve the follow diferential equation

#### alejandrito29

i need to solve the follow diferential equation:

$$(\frac{du}{dy})^2=A+Be^{2u}+C \sqrt{D+Ee^{4u}}$$

where A,B,C,D,E are nonzero.

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#### berkeman

Mentor
Re: help

i need to solve the follow diferential equation:

$$(\frac{du}{dy})^2=A+Be^{2u}+C \sqrt{D+Ee^{4u}}$$

where A,B,C,D,E are nonzero.
What is the context of the question? Is it for schoolwork?

#### alejandrito29

Re: help

What is the context of the question? Is it for schoolwork?
not, is for my thesis. I have tried make him.

#### kosovtsov

Re: help

Maple gives the following solution to your ODE (in implicit form)

$$\int_k^{u(y)}\frac{d\xi}{\sqrt{A+Be^{2\xi}+C\sqrt{D+Ee^{4\xi}}}}=\pm y,$$

where k is an arbitrary constant.

#### alejandrito29

Re: help

Maple gives the following solution to your ODE (in implicit form)

$$\int_k^{u(y)}\frac{d\xi}{\sqrt{A+Be^{2\xi}+C\sqrt{D+Ee^{4\xi}}}}=\pm y,$$

where k is an arbitrary constant.
obvious, separation variables, but

there is a way to find a explicit solution?

#### gato_

Re: help

Try $$z=e^{2\zeta}$$, then $$z=\sqrt(D/E)Sinh(\theta)$$. Maple manages to integrate that, but the resulting expression is nasty

#### alejandrito29

Re: help

Try $$z=e^{2\zeta}$$, then $$z=\sqrt(D/E)Sinh(\theta)$$. Maple manages to integrate that, but the resulting expression is nasty
$$2\zeta=ln(\sqrt(D/E)sinh(\theta))??????$$