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  • Find a particular solution satisfying the given condition: cos (dy/dx) = a (a belongs to R); y = 1 when x = 0

13. Find a particular solution satisfying the given condition:

       \cos\left(\frac{dy}{dx} \right ) = a\ (a\in R);\ y = 1\ \textup{when}\ x = 0

Answers (1)

best_answer

Given,

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

\\ \implies \frac{dy}{dx} = \cos^{-1}a \\ \implies \int dy = \int\cos^{-1}a\ dx \\ \implies y = x\cos^{-1}a + c

Now, y =1 when x =0

1 = 0 + c

Therefore, c = 1

Putting the value of c:

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

Posted by

HARSH KANKARIA

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