Find the particular solution, satisfying the given condition, for the following differential equation:
$\frac{dy}{dx} - \frac{y}{x} + cosec (\frac{y}{x}) = 0; y = 0 when x = 1$

Solution

$\frac{dy}{dx} - \frac{y}{x} + cosec (\frac{y}{x}) = 0 . . . . . . . (i) y = 0 When x = 1 Let \frac{y}{x} = t \Rightarrow y = xt \Rightarrow \frac{dy}{dx} = x \frac{dt}{dx} + t By substituting \frac{dy}{dx} in equation (i) (x \frac{dt}{dx} + t) - t + cosect = 0 \Rightarrow x \frac{dt}{dx} = - cosect \Rightarrow \int \frac{dt}{\cos ect} + \int \frac{dx}{x} = 0 \Rightarrow - cost + logx = C \Rightarrow - \cos (\frac{y}{x}) + logx = C$

Using y = 0 When x= 1

$- 1 + 0 = C \Rightarrow C = - 1 So the solution is : \cos (\frac{y}{x}) = logx + 1$

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Differential Equations

Find the particular solution, satisfying the given condition, for the following differential equation:
$\frac{dy}{dx} - \frac{y}{x} + cosec (\frac{y}{x}) = 0; y = 0 when x = 1$

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For Daily Free Study Material Join wiredfaculty

Differential Equations

Find the particular solution, satisfying the given condition, for the following differential equation:dydx - yx + cosec yx = 0 ; y = 0 when x = 1

Some More Questions From Differential Equations Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the particular solution, satisfying the given condition, for the following differential equation:
$\frac{dy}{dx} - \frac{y}{x} + cosec (\frac{y}{x}) = 0; y = 0 when x = 1$