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(dy/dx)^2-xdy/dx+y=0 is the given differential equation.what is the solution of given equation?

(dy/dx)^2-xdy/dx+y=0 is the  given differential equation.what is the solution of given equation?

Grade:12th pass

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
4 years ago
just differentiate the equation again and we will get
2(\frac{dy}{dx})(\frac{d^2y}{dx^2}) - x(\frac{d^2y}{dx^2}) - \frac{dy}{dx} + \frac{dy}{dx} = 0

this gets to
2(\frac{dy}{dx}) = x \quad \Rightarrow \quad y = x^2/4

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