Solve the following initial value problem:

Find: Find the particular solution of this differential equation.

On equating we get,

= cos y dy = e^x dx

Integrating both side

=

= sin y = e^x + C …..(i)

Put x = 0, y = π/2

=

= 1 = 1 + C

= C = 0

Put the value of C in equation (i)

Sin y = e^x

Hence, y = sin^-1(e^x)