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The differential equations , find the particular solution sati

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The differential equations , find the particular solution satisfying the given condition: $\frac{d y}{d x} - \frac{y}{x} + cos e c (\frac{y}{x}) = 0; y = 0$ when x = 1

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The differential equations , find the particular solution satisfying the given condition:

\frac{d y}{d x} - \frac{y}{x} + cos e c (\frac{y}{x}) = 0; y = 0

when x = 1

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Text solutionVerified

Solution:

\frac{d y}{d x} = \frac{y}{x} + cos e c \frac{y}{x} = f (x, y)

let y/x=t

\frac{d y}{d x} = t + \frac{x d t}{d x}

t + \frac{x a t}{d x} = t + cos e c t

\frac{x d t}{d x} = cos e c t

\int sin t d t = ln ∣ x ∣ + c

- cos t = ln ∣ x ∣ + c

given x=1 and y=0
c=-1

ln ∣ x ∣ + \frac{cos y}{x} = 1

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Question Text	The differential equations , find the particular solution satisfying the given condition: $\frac{d y}{d x} - \frac{y}{x} + cos e c (\frac{y}{x}) = 0; y = 0$ when x = 1
Answer Type	Text solution:1
Upvotes	150