How do I find an 'explicit formula' for a solution y(x), which also satisfies initial conditions y'(0) = 1 and y(0) = 0? - where the non-linear 2nd O.D.E is
*_*_*_*_*_* MERRY CHRISTMAS*_*_*_*_*_*
Thanks in advance
You can then rearrange to get:
Which is solveable by some fairly simple integration , don't forget to sub back into y.
Explicit just means you write it in the form
This works as a general rule btw. If there is no "y" term in your 2nd order ODE, then you can transform it into a first order ODE using substitution as shown above.
It's ridiculous to carry an arbitrary constant into the second integration when it's possible to get its value. Not the least reason being that the technique required for doing the second integration will depend on what the value of that first arbitrary constant is ....