The solution of the differential equation d y-d x-1-x-y-x y is -AISSE 1985- AI CBSE 1990- MP PET 2003-A- log 1-y-x-x2-2-cB- 1-y2-x-x2-2-cC- log 1-y-log 1-x-cD- None of these

The correct option is A dy/dx = 1 + x + y + xy ⇒dy/dx = (1 + x) (1 + y) ⇒dy/1+y = (1+x) dx On integrating, we get log (1+y) = x^2/2 + x + c. nbsp; ...

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Standard XII

Mathematics

Logarithmic Differentiation

The solution ...

Question

The solution of the differential equation $\frac{d y}{d x} = 1 + x + y + x y$ is
[AISSE 1985; AI CBSE 1990; MP PET 2003]

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None of these

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Solution

The correct option is A

$\frac{d y}{d x} = 1 + x + y + x y \Rightarrow \frac{d y}{d x} = (1 + x) (1 + y) \Rightarrow \frac{d y}{1 + y} = (1 + x) d x$
On integrating, we get log $(1 + y) = \frac{x^{2}}{2} + x + c .$

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Q. The general solution of the differential equation

\frac{d y}{d x} + y

g' (x) = g (x) g' (x), where g (x) is a given function of x, is
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\int \frac{1}{1 - \cos x - \sin x} d x =

(a)

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(b)

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(c)

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(d)

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The solution of the differential equation dydx=1+x+y+xy is [AISSE 1985; AI CBSE 1990; MP PET 2003]

The correct option is A dydx=1+x+y+xy⇒dydx=(1+x)(1+y)⇒dy1+y=(1+x)dx On integrating, we get log (1+y)=x22+x+c.

The solution of the differential equation $\frac{d y}{d x} = 1 + x + y + x y$ is
[AISSE 1985; AI CBSE 1990; MP PET 2003]

The correct option is A

$\frac{d y}{d x} = 1 + x + y + x y \Rightarrow \frac{d y}{d x} = (1 + x) (1 + y) \Rightarrow \frac{d y}{1 + y} = (1 + x) d x$
On integrating, we get log $(1 + y) = \frac{x^{2}}{2} + x + c .$