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in Differential Equations by (49.9k points)
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In differential equation show that it is homogeneous and solve it.

x\(\frac{dy}{dx}\) - y + xsin\(\frac{y}{x}\) = 0

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⇒ x\(\frac{dy}{dx}\) - y + xsin\(\frac{y}{x}\) = 0

⇒ the given differential equation is a homogenous equation. 

The solution of the given differential equation is : 

Put y = vx

Integrating both the sides we get:

Resubstituting the value of y = vx we get

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