The differential equation d x d y = y 1 − y 2 determines a family of circles with

d x d y = y 1 − y 2 ⇒ ∫ 1 − y 2 y d y = ∫ d x ⇒ − 1 − y 2 = x + C ⇒ ( x + c ) 2 + y 2 = 1 Centre ( − C , 0 ) and radius = 1 .

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Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationVariable separableEasy2 minPYQ_2007

MathematicsEasysingle choice

The differential equation $\frac{d y}{d x} = \frac{1 - y ^{2}}{y}$ determines a family of circles with

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Solution:

$\frac{d y}{d x} = \frac{1 - y ^{2}}{y} \Rightarrow \int \frac{y}{1 - y ^{2}} d y = \int d x \Rightarrow - 1 - y^{2} = x + C \Rightarrow (x + c)^{2} + y^{2} = 1$ Centre $(- C, 0)$ and radius $= 1$ .

Stream:JEE_ADVSubject:MathematicsTopic:Differential EquationSubtopic:Variable separable

⏱ 2mℹ️ Source: PYQ_2007

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