Solve the following initial value problem:

The given differential Equation is .

Find: Find the particular solution of this differential equation.

=

=

Now Integrating Both sides

=

=

= …..(1)

Put x = 1, y = 1

= 2 log(1)=5log(1) + C

= 0 = C

Put the value of C in equation (1)

= 2log |y| = 5log|x|

= y⁵ = |x|²

Hence, y = |x|^5/2