Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationVariable separableEasy2 minQB

MathematicsEasysingle choice

The family of curves passing through $(0, 0)$ and satisfying the differential equation $\frac{y _{2}}{y _{1}} = 1$ (where $y_{n} = d^{n} y / d x^{n})$ is

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Answer:

Solution:

$\frac{d p}{d x} = P ($ where $p = \frac{d y}{d x})$

$ln P = x + c \Rightarrow p = e^{x + c}$

$\frac{d y}{d x} = k e^{x} y = k e^{x} + λ$

Satisfying $(0, 0)$ , So $λ = - k$

$y = k (e^{x} - 1)$

Stream:JEESubject:MathematicsTopic:Differential EquationSubtopic:Variable separable

⏱ 2mℹ️ Source: QB

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