Question 11 of 96beginner💡 UnderstandMCQ1 mark

The degree of the differential equation

(d2ydx2)3+(dydx)2+sin⁡(dydx)+1=0\left(\frac{d^2 y}{dx^2}\right)^3 + \left(\frac{dy}{dx}\right)^2 + \sin \left(\frac{dy}{dx}\right) + 1 = 0
Exercise: EXERCISE 9.1 | Q: 11 | (Page 5)
For More Understanding

Explanation

According to the textbook context, to define the degree of a differential equation, it must be a polynomial equation in derivatives (y', y'', etc.). The context shows that equation (11): dy/dx + sin(dy/dx) = 0 is NOT a polynomial equation in y' because of the sine function, and therefore its degree cannot be defined. Similarly, in the given equation, the term sin(dy/dx) makes it a non-polynomial equation in derivatives. Since the equation contains sin(dy/dx), it is not a polynomial equation in y' and y'', hence the degree is not defined.

Solution Steps

  1. Step 1: Identify that for degree to be defined, the differential equation must be a polynomial equation in derivatives.

  2. Step 2: Examine the given equation and note the presence of sin(dy/dx) term.

  3. Step 3: Since sin(dy/dx) is not a polynomial term in the derivative y', the equation is not a polynomial equation in derivatives.

  4. Step 4: Therefore, the degree of this differential equation is not defined.

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