The solution of d y d x = y x + t a n y x is Options: A . &nbspy sin(yx)=cx B . &nbspy sin(yx)=cy C . &nbspsin(xy)=cx D . &nbspsin(yx)=cx

Answer: Option D : D Put y = v x . T h e n d y d x = v + x d v d x Given equation is d y d x = v x + t a n y x ⇒ v + x t a n v ⇒ c o t v d v = d x x ⇒ l o g s i n v = l o g x + l o g c ⇒ s i n v = c x ⇒ s i n ( y x = c x )

The solution of dydx=yx+tanyx is

Question

The solution of

\frac{d y}{d x} = \frac{y}{x} + t a n \frac{y}{x}

Options:

A . y sin(yx)=cx

B . y sin(yx)=cy

C . sin(xy)=cx

D . sin(yx)=cx

Answer: Option D
:
D
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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