Question:medium
The solution of the differential equation $\frac{x \frac{dy}{dx} - y}{\sqrt{x^2 - y^2}} = 10x^2$ is:
The solution of the differential equation $\frac{x \frac{dy}{dx} - y}{\sqrt{x^2 - y^2}} = 10x^2$ is:
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The expression $\frac{xdy-ydx}{x^2}$ always suggests the substitution $v=\frac{y}{x}$.
Updated On: May 2, 2026
- $\sin^{-1} \left( \frac{y}{x} \right) - 5x^2 = C$
- $\sin^{-1} \left( \frac{y}{x} \right) = 10x^2 + C$
- $\frac{y}{x} = 5x^2 + C$
- $\sin^{-1} \left( \frac{y}{x} \right) = 10x^2 + Cx$
- $\sin^{-1} \left( \frac{y}{x} \right) + 5x^2 = C$
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The Correct Option is A
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