The solution of the differential equation x4d y-d x-x3 y-cosecx y-0 is equal to A- 2 cos x y-x-2-cB- 2 cos x y-y-2-cC- 2 sin x y-x-2-cD- 2 sin x y-y-2-c

The correct option is A 2 cos(xy)+x^ 2=c x^4 dy/dx+x^3 y +cosec(xy)=0 x^4 dy+x^3 y dx +cosec(xy)dx=0 x^3 (x dy +y dx)+cosec(xy)dx=0 x^3 d(xy)+cosec(xy)dx= ...

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Standard XII

Mathematics

Variable Separable Method

The solution ...

Question

The solution of the differential equation $x^{4} \frac{d y}{d x} + x^{3} y + c o s e c (x y) = 0$ is equal to

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

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

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2 s i n (x y) + x^{- 2} = c

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2 s i n (x y) + y^{- 2} = c

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Solution

The correct option is A $2 c o s (x y) + x^{- 2} = c$

$x^{4} \frac{d y}{d x} + x^{3} y + c o s e c (x y) = 0 x^{4} d y + x^{3} y d x + c o s e c (x y) d x = 0 x^{3} (x d y + y d x) + c o s e c (x y) d x = 0 x^{3} d (x y) + c o s e c (x y) d x = 0 \frac{d (x y)}{c o s e c (x y)} + \frac{d x}{x^{3}} = 0$
Integrating both sides, $\int \frac{d (x y)}{c o s e c (x y)} + \int \frac{d x}{x^{3}} = 0$
$\int s i n (x y) d (x y) + \int x^{- 3} d x = 0 - c o s (x y) + (\frac{x^{- 2}}{- 2}) = c; 2 c o s (x y) + x^{- 2} = c$ .

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The solution of the differential equation x4dydx+x3y+cosec(xy)=0 is equal to

The correct option is A 2cos(xy)+x−2=c x4dydx+x3y+cosec(xy)=0x4dy+x3ydx+cosec(xy)dx=0x3(xdy+ydx)+cosec(xy)dx=0x3d(xy)+cosec(xy)dx=0d(xy)cosec(xy)+dxx3=0 Integrating both sides,∫d(xy)cosec(xy)+∫dxx3=0 ∫sin(xy)d(xy)+∫x−3dx=0−cos(xy)+(x−2−2)=c;2cos(xy)+x−2=c.

The solution of the differential equation $x^{4} \frac{d y}{d x} + x^{3} y + c o s e c (x y) = 0$ is equal to