(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that w(t) = tanh(t) solves the nonlinear problem:

w''(t)+2w(t)-2w^{3}(t) = 0

t ε ℝ

2. Relevant equations

[itex]\frac{d^2tanh(t)}{dt^2}[/itex] = -2tanh(t)sech^{2}(t) = [itex]\frac{-8sinh(2t)cosh^2(t)}{(cosh(2t)+1)^3}[/itex]

tanh(t) = [itex]\frac{sinh(2t)}{cosh(2t)+1}[/itex]

tanh(t)^{3}= [itex]\frac{sinh^3(2t)}{(cosh(2t)+1)^3}[/itex]

3. The attempt at a solution

plug and chug? I'm not good at hyperbolic functions.

Any ideas?

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# Homework Help: Non-linear differential equations!

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