Question

Sinx dy/dx + 3y = cosx

Answer 1

Answer:

Step-by-step explanation:

dy/dx+3y/sinx=cotx

i.f=e^∫(3/sinx)dx

if=e^3ln9tanx/2

if*y=∫if*cotx

Answer 2

we have to differentiate the following expression :-✅

$\rm 2x + 3 {y}^{2} = cos \: x$

$\rm 3 {y}^{2} = cos \: x - 2x$

$\rm {y}^{2} = \dfrac{cos \: x - 2x}{3} \\ \\ \rm {y} = \sqrt{\dfrac{cos \: x - 2x}{3}} ...(1)$

$\rm \longrightarrow 3 \dfrac{d( {y}^{2})}{dx} = \dfrac{d( cos \: x - 2x)}{dx}$

$\rm \longrightarrow 6y \dfrac{d{y}}{dx} = - sinx - 2 \\ \\\rm \longrightarrow 6y \dfrac{d{y}}{dx} = -( sinx + 2 ) \\ \\\rm \longrightarrow \dfrac{d{y}}{dx} = \dfrac{-( sinx + 2 )}{6y}$

You can put the value of y from equation (1).

Answer :-

$\rm\dfrac{d{y}}{dx} = \dfrac{-( sinx + 2 )}{6y}$✅