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( D Y D X ) 2 + 1 D Y / D X = 2 - Mathematics

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प्रश्न

\[\left( \frac{dy}{dx} \right)^2 + \frac{1}{dy/dx} = 2\]
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उत्तर

\[\left( \frac{dy}{dx} \right)^2 + \frac{1}{\left( \frac{dy}{dx} \right)} = 2\]

\[\Rightarrow \frac{\left( \frac{dy}{dx} \right)^3 + 1}{\left( \frac{dy}{dx} \right)} = 2\]
\[\Rightarrow \left( \frac{dy}{dx} \right)^3 - 2\frac{dy}{dx} + 1 = 0\]
In this equation, the order of the highest order derivative is 1 and its highest power is 3. So, it is a differential equation of order 1 and degree 3.
It is a non-linear differential equation because the differential coefficient \[\frac{dy}{dx}\]  has exponent 3, which is greater than 1.
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अध्याय 22: Differential Equations - Exercise 22.01 [पृष्ठ ५]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 22 Differential Equations
Exercise 22.01 | Q 3 | पृष्ठ ५

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