The particular solution of ≤ft(dy/dx) = a (where, a R), (y=2 when x=0 ), is

Correct Answer is : cos⁡(y−2x)=a ≤ft(y-2/x) = acos(xy−2)=a

Correct Answer is : cos⁡(y−2x)=a ≤ft(y-2/x) = acos(xy−2)=a

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CGPET 2013 Solved Paper

Section: Mathematics

Question : 108 of 150

Marks: +1, -0

\cos \left(\frac{dy}{dx}\right) = a

a \in R), (y=2

x=0

Solution:

Given, differential equation is

\;\cos \left(\frac{dy}{dx}\right) = a

\Rightarrow \; \frac{dy}{dx} = \cos^{-1} a

\Rightarrow \; dy = \cos^{-1} \; \text{adx} \;

\;

On integrating both sides, we get

\int dy = \cos^{-1} a \int dx + C

\Rightarrow \; y = \cos^{-1} a x + C

. . . (i)

When

\; x = 0

, then

y = 2

Then, from Eq. (i), we get

2 = 0 + C \Rightarrow C = 2

On putting the value of

C

in Eq. (i), we get

y = x \cos^{-1} a + 2

\Rightarrow \; y-2 = x \cos^{-1} a

\Rightarrow \; \frac{y-2}{x} = \cos^{-1} a

\Rightarrow \cos \left(\frac{y-2}{x}\right) = a

which is the required solution.

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