The solution of d y d x + P ( x ) y = 0 is:

Question

The solution of $\frac{d y}{d x} + P (x) y = 0$ is:

Smart Achievers · Accepted Answer

(3)

Ans. $y = C e^{- \int P d x}$

Explanation:

$\frac{d y}{d x} + P (x) y = 0$

Here, $Q = 0$

$∴$ $I . F . = e^{\int P d x}$

$∴$ Solution of the given equation is

$y (I . F .) = \int Q (I . F .) d x + C$

$\Rightarrow$ $y e^{\int P d x} = 0 + C$

$\Rightarrow$ $y = C e^{- \int P d x}$

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