Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationApplication (Mixing, Geometric, temp., trajectory)Easy2 minQB

MathematicsEasysingle choice

An equation of the curve in which subnormal varies as the square of the ordinate is ( $k$ is constant of proportionality)

Options:

Answer:

Solution:

According to the given condition $y \frac{d y}{d x} = k y^{2}$

$\Rightarrow \frac{d y}{y} = k d x$ (variables separable equation) $\Rightarrow lo g ∣ y ∣ = k x + C \Rightarrow ∣ y ∣ = B e^{k x} \Rightarrow y = A e^{k x}$ where $A = \pm B$ and $k$ is the constant of proportionality.

Stream:JEESubject:MathematicsTopic:Differential EquationSubtopic:Application (Mixing, Geometric, temp., trajectory)

⏱ 2mℹ️ Source: QB

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