The equation of the curve which passes through the point 1-1 and whose slope is given by 2 y-x- is A- y-x2B- x2-y2-0C- 2 x 2- y 2-3D- None of these

The correct option is A y =x^2Slope dy/dx=2y/x ⇒ 2 ∫dx/x= ∫dy/y⇒ 2 log x = log y + log c ⇒ x^2 =ye Since it passes through (1, 1), therefore c =1 Hence x^2 y ...

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Byju's Answer

Standard XII

Mathematics

Formation of a Differential Equation from a General Solution

The equation ...

Question

The equation of the curve which passes through the point (1, 1) and whose slope is given by $\frac{2 y}{x}$ , is

y = x^{2}

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x^{2} - y^{2} = 0

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2 x^{2} + y^{2} = 3

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N o n e o f t h e s e

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Solution

The correct option is A $y = x^{2}$
Slope $\frac{d y}{d x} = \frac{2 y}{x}$
$\Rightarrow 2 \int \frac{d x}{x} = \int \frac{d y}{y} \Rightarrow 2 l o g x = l o g y + l o g c \Rightarrow x^{2} = y e$
Since it passes through (1, 1), therefore c =1
Hence $x^{2} - y = 0 \Rightarrow y = x^{2}$ .

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The equation of the curve which passes through the point (1, 1) and whose slope is given by 2yx, is

The correct option is A y=x2Slope dydx=2yx ⇒2∫dxx=∫dyy⇒2logx=logy+logc⇒x2=ye Since it passes through (1, 1), therefore c =1 Hence x2−y=0⇒y=x2.

The equation of the curve which passes through the point (1, 1) and whose slope is given by $\frac{2 y}{x}$ , is

The correct option is A $y = x^{2}$
Slope $\frac{d y}{d x} = \frac{2 y}{x}$
$\Rightarrow 2 \int \frac{d x}{x} = \int \frac{d y}{y} \Rightarrow 2 l o g x = l o g y + l o g c \Rightarrow x^{2} = y e$
Since it passes through (1, 1), therefore c =1
Hence $x^{2} - y = 0 \Rightarrow y = x^{2}$ .