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
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