D 3 Y D X 3 + ( D 2 Y D X 2 ) 3 + D Y D X + 4 Y = Sin X - Mathematics

प्रश्न

\[\frac{d^3 y}{d x^3} + \left( \frac{d^2 y}{d x^2} \right)^3 + \frac{dy}{dx} + 4y = \sin x\]

उत्तर

\[\frac{d^3 y}{d x^3} + \left( \frac{d^2 y}{d x^2} \right)^3 + \frac{dy}{dx} + 4y = \sin x\]
In this differential equation, the order of the highest order derivative is 3 and its power is 1. So, it is a differential equation of degree 3 and order 1.
It is a non-linear differential equation, as its differential co-efficient \[\frac{d^2 y}{d x^2}\] has exponent 3, which is greater than 1.

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Order and Degree of a Differential Equation

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Q 12 Q 11 Q 13

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 12 | पृष्ठ ५

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