dy-dx 2 - x-y dy-dx - xy-0

The correct option is D all the above ( nbsp;dy/dx )^2 (x+y) nbsp;dy/dx + xy=0 ⇒ ( nbsp;dy/dx y ) ( nbsp;dy/dx x ) = 0 ...

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Byju's Answer

Standard X

Chemistry

Atomic Radius

dy/dx 2 - x+y...

Question

${(\frac{d y}{d x})}^{2} - (x + y) \frac{d y}{d x} + x y = 0$

y = k e^{x}

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y = \frac{x^{2}}{2} + c

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ln y = x + c

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all the above

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Solution

The correct option is D all the above
${(\frac{d y}{d x})}^{2} - (x + y) \frac{d y}{d x} + x y = 0$
$\Rightarrow (\frac{d y}{d x} - y) (\frac{d y}{d x} - x) = 0$
$\Rightarrow \frac{d y}{d x} = y$ or $\frac{d y}{d x} = x$
$\Rightarrow ln y = x + c$ or $y = \frac{x^{2}}{2} + c$
$\Rightarrow y = k e^{x}$

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(dydx)2−(x+y)dydx+xy=0

The correct option is D all the above(dydx)2−(x+y)dydx+xy=0⇒(dydx−y)(dydx−x)=0⇒dydx=y or dydx=x⇒lny=x+c or y=x22+c⇒y=kex

${(\frac{d y}{d x})}^{2} - (x + y) \frac{d y}{d x} + x y = 0$