How would you do this:
solve:
y^2dy - 3x^5dx = 0
the answer in the book is 2y^3 = 3x^6 + C
I am clueless how to do these types of problems. The book doesnt explain it clearly and my notes arent helping me. Thanks.
Exactly like the other one:
$\displaystyle
y^2dy - 3x^5dx = 0
$
so:
$\displaystyle
\int y^2dy - \int 3x^5dx = K
$
$\displaystyle
\frac{y^3}{3} - \frac{x^6}{2} = K
$
Now multiply through by 6:
$\displaystyle
2y^3 - 3x^6 = C
$
(the constant $\displaystyle K$ has now been replaced by the constant $\displaystyle C=6K$)
Reaarange and you have the result.
RonL