The solution of d t d v + m k v = − g is

d t d v + m K v = − g Integrating factor (I.F.) = e ∫ m k d t = e m K t ∴ V e m K t = − ∫ g e K . t / m + c V e m K t = K − g m e m K t + c V = C ⋅ e m − K t − K m g

Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationLinear DE / Red. LDEEasy2 minQB

MathematicsEasysingle choice

The solution of $\frac{d v}{d t} + \frac{k}{m} v = - g$ is

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Answer:

Solution:

$\frac{d v}{d t} + \frac{K}{m} v = - g$

Integrating factor (I.F.) $= e^{\int \frac{k}{m} d t} = e^{\frac{K}{m} t}$

$∴ V e^{\frac{K}{m} t} = - \int g e^{K . t / m} + c$

$V e^{\frac{K}{m} t} = \frac{- g m}{K} e^{\frac{K}{m} t} + c$

$V = C \cdot e^{\frac{- K}{m} t} - \frac{m g}{K}$

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

⏱ 2mℹ️ Source: QB

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