Fine linear equation for- cosdydx-aa- R- y-2 when x-0-

cos #160; ( dy / dx #160; ) =a at y=0,x 0 dy / dx =cos #160; _ a ^ 1 dx dy=dx cos #160; _ a ^ 1 dx int egrate ...

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Standard XII

Mathematics

Solving Linear Differential Equations of First Order

Fine linear e...

Question

Fine linear equation for,
$cos (\frac{d y}{d x}) = a (a \in R); y = 2$ when $x = 0$ .

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Solution

$\begin{matrix} cos (\frac{d y}{d x}) = a a t y = 0, x - 0 \frac{d y}{d x} = {cos}_{a}^{- 1} d x d y = d x cos_{a}^{- 1} d x i n t e g r a t e o n b o t h s i d e \int d y = {cos}_{a}^{- 1} \int d x y = x {cos}_{a}^{- 1} + c P u t y = 0 a n d x = 0 0 = 0 + c, c = 0 ∴ y = x {cos}_{a}^{- 1} A n s . \end{matrix}$

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cos (\frac{d y}{d x}) = a (a \in R); y = 1

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x = 0

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For the differential equation in given question find a particular solution satisfying the given condition.

$c o s (\frac{d y}{d x}) = a (a ϵ R), y = 2 w h e n x = 0.$

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cos (\frac{d y}{d x}) = a, (a \in R)

Q. For each of the following differential equations, find a particular solution satisfying the given condition:
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\cos (\frac{d y}{d x}) = a, y = 1 when x = 0

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cos (\frac{d y}{d x}) = a; y = 1, x = 0

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Fine linear equation for, cos(dydx)=a(a∈R);y=2 when x=0.

cos(dydx)=aaty=0,x−0dydx=cos−1adxdy=dxcos−1adxintegrateonbothside∫dy=cos−1a∫dxy=xcos−1a+cPuty=0andx=00=0+c,c=0∴y=xcos−1aAns.

Fine linear equation for,
$cos (\frac{d y}{d x}) = a (a \in R); y = 2$ when $x = 0$ .