Question

I.F of $ylogy\frac{dx}{dy}+x=logy$ is:

• A. $log\left(logy\right)$
• B. $\frac{1}{logy}$
• C. $logy$
• D. $\frac{1}{log\left(logy\right)}$

Answer 1

The correct option is C $logy$

$I.F=e^{\int P\left(y\right)dy}$

$P\left(y\right)=\frac{1}{ylogy}$

$I.F=e^{\int \frac{1}{ylogy}dy}$...............(i)

let $logy=t$

$\Rightarrow \frac{1}{y}dy=dt$

Eq. (i) becomes

$\Rightarrow \int \frac{dt}{t}=logt$

$\therefore$ the $I.F.$ becomes

$\Rightarrow I.F=e^{loglogy}$$=logy$