Question

The solution of $(x+2y^3)\frac{dy}{dx}=y$ is:

• A. $y=x^3+cx$
• B. $x=y^3+cy$
• C. $x=y^2+cy$
• D. $y=x^3+c{y}^2$

Answer 1

Answer: (B)

$x=y^3+cy$

$\Rightarrow \frac{dx}{dy}=\frac{x}{y}+2y^2$

$\Rightarrow \frac{dx}{dy}-\frac{x}{y}=2y^2$

I.F=$e^{{\int }^{-}1{/}_{y}dy}=e^{-}logy=1{/}_y$

$\Rightarrow \frac{1}{y}\frac{dx}{dy}-x/y^2=2y$

$\Rightarrow \frac{d}{dy}{(}^x{/}_y)=2y$

$\Rightarrow \int d{(}^x{/}_y)=\int 2ydy+c$

${\Rightarrow }^x{/}_y=y^2+c$

$x=y^3+cy$