Question

What is the solution of DE $\left(\frac{y}{x}+\sin y\right)\mathrm{dx}+\left(\log x+x\cos y\right)\mathrm{dy}=0$

• A. y sin x + x log y =k
• B. y log x + x sin y = k
• C. log x + sin y = k
• D. log y + sin x = k

Answer 1

The correct option is B y log x + x sin y = k

$\left(\frac{y}{x}+\sin y\right)\mathrm{dx}+\left(\log x+x\cos y\right)\mathrm{dy}=0\left(\frac{y}{x}\mathrm{dx}+\log x\mathrm{dy}\right)+\left(\sin y\mathrm{dx}+x\cos y\mathrm{dy}\right)=0d\left(y\log x\right)+d\left(x\sin y\right)=0d(y\log x+x\sin y)=0y\log x+x\sin y=k$