Solve the differential equation: y'= sqrtx * y

y' = sqrtx * y

To solve
differential equation, first we will rewrite the
equation:

we know that y' =
dy/dx

==> dy / dx = sqrtx *
y

Now we will group x terms on one side and y terms on the
other side of the equality:

We will multiply by dx/y for
both sides:

==> dy/y = sqrtx
dx

Now let us integrate both
sides:

intg dy/y = intg sqrtx
dx

==> ln y = (x^3/2 )/(3/2) +
C

==> ln y =( 2/3)(x^3/2) +
C

==> y= e^[(2/3)*x^3/2)+
C]

==> y = e^(2/3)x^3/2  + C