The solution of d y-d x-y-x-tany-x is

The correct option is C sin (y/x) = cxPut y = vx. Then dy/dx = v+x dv/dx Given equation is dy/dx = v/x + tan y/x⇒ v + x tan v ⇒ cot v dv = dx/x⇒ log sin v= log ...

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Standard XII

Mathematics

Solving Homogeneous Differential Equations

The solution ...

Question

The solution of $\frac{d y}{d x} = \frac{y}{x} + t a n \frac{y}{x}$ is

y s i n (\frac{y}{x}) = c x

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y s i n (\frac{y}{x}) = c y

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s i n (\frac{x}{y}) = c x

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s i n (\frac{y}{x}) = c x

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Solution

The correct option is D $s i n (\frac{y}{x}) = c x$
Put $y = v x . T h e n \frac{d y}{d x} = v + x \frac{d v}{d x}$
Given equation is $\frac{d y}{d x} = \frac{v}{x} + t a n \frac{y}{x} \Rightarrow v + x t a n v \Rightarrow c o t v d v = \frac{d x}{x} \Rightarrow l o g s i n v = l o g x + l o g c$
$\Rightarrow s i n v = c x \Rightarrow s i n (\frac{y}{x} = c x)$

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The solution of dydx=yx+tanyx is

The correct option is D sin(yx)=cxPut y=vx.Thendydx=v+xdvdx Given equation is dydx=vx+tanyx⇒v+x tan v⇒cot v dv=dxx⇒log sin v=log x+logc ⇒sin v=cx⇒sin(yx=cx)

The solution of $\frac{d y}{d x} = \frac{y}{x} + t a n \frac{y}{x}$ is