Question

the differential equation (3+bycosx)dx + (2sinx-4y3)dy=0 is exact if then b=

Answer 1

Answer:

If the given differential equation is exact,the value of b is 2

Step-by-step explanation:

The given differential equation is

$(3 + bycosx)dx + (2sinx - 4y {}^{3})dy = 0$

The given differential equation is of form

$Mdx+Ndy=0$

For the differential equation to be exact,the conditions are

$\frac{dM}{dy}=\frac{dN}{dx}$

$\frac{dM}{dy}= \frac{d}{dy} (3 + bycosx) = bcosx$

Similarly,

$\frac{dN}{dx} = \frac{d}{dx} (2sinx - 4 {y}^{3} ) = 2cosx$

Therefore,for exact differential equation,

$bcosx = 2cosx \\ = > b = 2$

Therefore,If the given differential equation is exact,the value of b is 2

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