**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

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!