The solution of frac{dy}{dx} + frac{y}{3} = 1 | vedclass

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(B) The given differential equation is a linear differential equation of the form $\frac{dy}{dx} + Py = Q$,where $P = \frac{1}{3}$ and $Q = 1$.First,w

Vedclass · Accepted Answer

$y = 3 + ce^{-x/3}$

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(B) The given differential equation is a linear differential equation of the form $\frac{dy}{dx} + Py = Q$,where $P = \frac{1}{3}$ and $Q = 1$.First,we find the integrating factor $(I.F.)$:$I.F. = e^{\int P dx} = e^{\int \frac{1}{3} dx} = e^{x/3}$.The general solution is given by $y \cdot (I.F.) = \int Q \cdot (I.F.) dx + c$.Substituting the values:$y \cdot e^{x/3} = \int 1 \cdot e^{x/3} dx + c$.Integrating the right side:$y \cdot e^{x/3} = 3e^{x/3} + c$.Dividing both sides by $e^{x/3}$:$y = 3 + c e^{-x/3}$.

The solution of $\frac{dy}{dx} + \frac{y}{3} = 1$ is

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