Question

The general solution of the differential equation $\frac{dy}{dx}+y\cot x=\csc x$, is

• A. $x+ysinx=C$
• B. $x+ycosx=C$
• C. $y+x\left(\sin x+\cos x\right)$
• D. $y\sin x=x+C$

Answer 1

The correct option is D $y\sin x=x+C$

$\frac{dy}{dx}+y\cot x=cosecn$

$I.F=e^{\int \omega txdx}=e^{en\left(\sin n\right)}$

$=\sin n$

$y\cdot \sin x=\int cosecx.mn-dx+c$

$y\sin n=x+c$

$\ne y\sin x=x+c$.