Question

Solution of x= 1+xy $\left(\frac{dy}{dx}\right)+\frac{x^2{y}^2}{2!}{\left(\frac{dy}{dx}\right)}^2+........is$

• A. y= log x + c
• B. $y^2={\left(\log x\right)}^2+c$
• C. y= log(x)+ xy
• D. $xy=x^y+c$

Answer 1

Answer: (B)

$y^2={\left(\log x\right)}^2+c$

$\Rightarrow x=e^{xy\frac{dy}{dx}}$

$\Rightarrow lnx=xy\frac{dy}{dx}$

$\Rightarrow ydy=\frac{lnx}{x}dx$

Integrate on both sides

$\Rightarrow \frac{y^2}{2}=\frac{(lnx{)}^2}{2}+c$

$\Rightarrow y^2=(logx{)}^2+c$