First slide

Methods of solving first order first degree differential equations

Question

$The solution of the differential equation \frac{dy}{dx} = \sin (x + y) \tan (x + y) - 1 is$

Moderate

A

$cosec(x+y)+tan(x+y)=x+c$
B

$x+cosec(x+y)=c$
C

$x+tan(x+y)=c$
D

$x+sec(x+y)=c$

Solution

$\begin{array}{l} Put x + y = t \to 1 + \frac{dy}{dx} = \frac{dt}{dx} \\ \Rightarrow \int cosectcott d t = \int d x \\ \Rightarrow - cosec (x + y) + c = x \end{array}$

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