Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationHomogeneous equation / Red. HDEMedium2 minQB

MathematicsMediumsingle choice

An equation of the curve satisfying $x d y - y d x = x^{2} - y^{2} d x$ and $y (1) = 0$ is

Answer:

Solution:

The equation can be written as $x^{2} \frac{x d y - y d x}{x ^{2}} = x 1 - (y / x)^{2} d x$

$\Rightarrow \frac{d ( y / x )}{1 - ( y / x ) ^{2}} = \frac{d x}{x} \Rightarrow sin^{- 1} y / x = lo g ∣ x ∣ + co n s t$

Since $y (1) = 0$ so const $= 0$ . Hence $y = x sin (lo g ∣ x ∣)$ .

Stream:JEESubject:MathematicsTopic:Differential EquationSubtopic:Homogeneous equation / Red. HDE

⏱ 2mℹ️ Source: QB

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