Hi

Can you tell me if i am correct in my method?

thanks

John

Separate the variables and find the indefinite integrals.

$\displaystyle \frac{dy}{dx}=y(x^3-x^\frac{1}{2})$

re-arrange to get y on left hand side and x on right hand side

$\displaystyle dy=y(x^3-x^\frac{1}{2})\cdot\ dx$

$\displaystyle \frac{1}{y} \cdot\ dy=(x^3-x^\frac{1}{2})\cdot\ dx$

Now integrate both sides:

$\displaystyle \int \frac{1}{y} \cdot\ dy=\int (x^3-x^\frac{1}{2})\cdot\ dx$

$\displaystyle lny=\frac{x^4}{4}-\frac{2}{3}x^\frac{3}{2} +C $

$\displaystyle y=e^{\frac{x^4}{4}-\frac{2}{3}x^\frac{3}{2} +C }$

$\displaystyle y= e^{\frac{x^4}{4}}-e^{\frac{2}{3}x^\frac{3}{2}}+e^{c} $

As $\displaystyle e^C=C$

$\displaystyle y= e^{\frac{x^4}{4}}-e^{\frac{2}{3}x^\frac{3}{2}}+C$

$\displaystyle y=e^{\frac{x^4}{4}-\frac{2}{3}x^\frac{3}{2}} +C $

Can you tell me if i am on track?