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i need to solve the follow diferential equation:
[tex](\frac{du}{dy})^2=A+Be^{2u}+C \sqrt{D+Ee^{4u}}[/tex]
where A,B,C,D,E are nonzero.
[tex](\frac{du}{dy})^2=A+Be^{2u}+C \sqrt{D+Ee^{4u}}[/tex]
where A,B,C,D,E are nonzero.
What is the context of the question? Is it for schoolwork?i need to solve the follow diferential equation:
[tex](\frac{du}{dy})^2=A+Be^{2u}+C \sqrt{D+Ee^{4u}}[/tex]
where A,B,C,D,E are nonzero.
not, is for my thesis. I have tried make him.What is the context of the question? Is it for schoolwork?
obvious, separation variables, butMaple gives the following solution to your ODE (in implicit form)
[tex] \int_k^{u(y)}\frac{d\xi}{\sqrt{A+Be^{2\xi}+C\sqrt{D+Ee^{4\xi}}}}=\pm y,[/tex]
where k is an arbitrary constant.
[tex]2\zeta=ln(\sqrt(D/E)sinh(\theta))??????[/tex]Try [tex]z=e^{2\zeta}[/tex], then [tex]z=\sqrt(D/E)Sinh(\theta)[/tex]. Maple manages to integrate that, but the resulting expression is nasty