Hi everybody, I am trying to solve two equations.
y'[x] = (r y[x])/x^2 with y[1] = a
which has a solution a*E^(r - r/x)
and
y'[x] = Sin[x] y[x] with y[0] = a
which has a solution a*E^(1 - Cos[x])
For the first one I wrote something like
We have
y'[x] = (r y[x])/x^2
Hence, y[x] = e^(-r/x) + c
where c is constant
Our y[1] = a
We are given in the output that
a*E^(r - (r/x))
Then the derivative of our output is
are^(r-(r/x))/x^2
In turn
are^(r-(r/x))/x^2
Then I stumbled
For the second one, I wrote similar logic ans stumbled too.
Can somebody please give a tip on how to approach it?
Thanks!
y'[x] = (r y[x])/x^2 with y[1] = a
which has a solution a*E^(r - r/x)
and
y'[x] = Sin[x] y[x] with y[0] = a
which has a solution a*E^(1 - Cos[x])
For the first one I wrote something like
We have
y'[x] = (r y[x])/x^2
Hence, y[x] = e^(-r/x) + c
where c is constant
Our y[1] = a
We are given in the output that
a*E^(r - (r/x))
Then the derivative of our output is
are^(r-(r/x))/x^2
In turn
are^(r-(r/x))/x^2
Then I stumbled
For the second one, I wrote similar logic ans stumbled too.
Can somebody please give a tip on how to approach it?
Thanks!