The integrating factor of the differential equation ( x 2 − 1 d x d y + 2 ) x y = x is

Given differential equation is ( x 2 − 1 ) d x d y + 2 x y = x ⇒ d x d y + x 2 − 1 2 x ⋅ y = x 2 − 1 x This is in linear form. Integrating factor = ∫ x 2 − 1 2 x d x = ∫ e t d t where = x 2 − 1 = e l o g t = x 2 − 1 Hence, required integrating factor = x 2 − 1 .

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MathematicsDifferential EquationLinear DE / Red. LDEEasy2 minPYQ_2012

MathematicsEasynumerical range

The integrating factor of the differential equation $(x^{2} - 1 \frac{d y}{d x} + 2) x y = x$ is

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Given differential equation is $(x^{2} - 1) \frac{d y}{d x} + 2 x y = x \Rightarrow \frac{d y}{d x} + \frac{2 x}{x ^{2} - 1} \cdot y = \frac{x}{x ^{2} - 1}$ This is in linear form. $Integrating factor = \int \frac{2 x}{x ^{2} - 1} d x = \int_{e} \frac{d t}{t} where = x^{2} - 1 = e^{l o g t} = x^{2} - 1$ Hence, required integrating factor $= x^{2} - 1$ .

Stream:JEESubject:MathematicsTopic:Differential EquationSubtopic:Linear DE / Red. LDE

⏱ 2mℹ️ Source: PYQ_2012

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