- #1
crybllrd
- 120
- 0
Homework Statement
Show that
[tex]y=tanh(t)[/tex]
satisfies the differential equation
[itex]\frac{dy}{dt}=1-y^{2}[/itex]
with initial conditions y(0) = 0
Homework Equations
The Attempt at a Solution
I'm not sure how to start, but we have only dealt with one D.E., and we had moved all the variables to a respective side then integrated.
[itex]dy=(1-y^{2})dt[/itex]
[itex]\frac{dy}{1-y^{2}}=dt[/itex]
Integrate both sides to get
[itex]ln|1-y^{2}|=t[/itex]
Not sure where to go from here