The general solution of the differential equation $y d x - x d y + x^{2} . sin y d y + (1 + x^{2}) d x = 0$ , is equal to:

x^{2} = (c + 1) x + x . c o s y - y

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x^{2} = (c + 1) x + x . c o s y + y

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x^{2} = c x + x . c o s y + y - 1

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x^{2} = c x + x . c o s y + y + 1

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Solution

The correct option is A $x^{2} = (c + 1) x + x . c o s y - y$
$y d x - x d y + x^{2} \cdot sin y d y + (1 + x^{2}) d x = 0$
Dividing by $x^{2}$ , we get
$\to sin y d y + \frac{1 + x^{2}}{x^{2}} d x = \frac{x d y - y d x}{x^{2}}$
$sin y d y + (\frac{1}{x^{2}} + 1) d x = d (\frac{y}{x})$
$\to$ Now by integrating, we get
$\to - cos y + \frac{- 1}{x} + x = \frac{y}{x} + C$
$\to x^{2} = (C + 1) x + x \cdot cos y - y$

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The general solution of the differential equation ydx−xdy+x2.sinydy+(1+x2)dx=0, is equal to:

The correct option is A x2=(c+1)x+x.cosy−yydx−xdy+x2⋅sinydy+(1+x2)dx=0Dividing by x2, we get→sinydy+1+x2x2dx=xdy−ydxx2sinydy+(1x2+1)dx=d(yx)→ Now by integrating, we get→−cosy+−1x+x=yx+C→x2=(C+1)x+x⋅cosy−y

The general solution of the differential equation $y d x - x d y + x^{2} . sin y d y + (1 + x^{2}) d x = 0$ , is equal to: