- #1

byrnesj1

- 7

- 0

## Homework Statement

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

w''(t)+2w(t)-2w

^{3}(t) = 0

t ε ℝ

## Homework 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]

## The Attempt at a Solution

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

Any ideas?

Last edited: