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1. ⇒ (MHT CET 2021 21th September Evening Shift )

$I : y^{'} = \frac{y + x}{x}; II : y^{'} = \frac{x^{2} + y}{x^{3}}; III : y^{'} = \frac{2 x y}{y^{2} - x^{2}}$

S1 : Differential equations given by I and II are homogeneous differential equations.

S2 : Differential equations given by II and III are homogeneous differential equations.

S3 : Differential equations given by I and III are homogeneous differential equations.

A. only S1 is valid

B. both S1 and S2 are valid

C. only S3 is valid

D. only S2 is valid.

Correct Option is (C)

We will check all 3 equations.

I $: \frac{d y}{d x} = \frac{y + x}{x} \Rightarrow$ All terms have same degree equal to 1 .

II $: \frac{d y}{d x} = \frac{x^{2} + y}{y^{3}} \Rightarrow$ Here all terms have different degrees.

III $: \frac{d y}{d x} = \frac{2 x y}{y^{2} - x^{2}} \Rightarrow$ All terms have same degree equal to 2 .

⇒Defferential Equation