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Explain solution RD Sharma class 12 chapter 21 Differential Equation exercise Fill in the blank question 28 maths

Answers (1)

Answer:

 Degree = 3

Hint:

 To find the degree of differential equation representing the family of curves y = Ax + A3,we have to eliminate the constant A.

Given:

 The degree of differential equation representing the family of curves y = Ax + A3, where A is arbitrary constant is ______

Solution:

\begin{aligned} &y=Ax + A^{3} \qquad \qquad \dots (i) \\ &\frac{\mathrm{d} y}{\mathrm{d} x}=A\qquad \qquad \dots (ii) \end{aligned}

Using the eqn (ii) in (i), we get

\begin{aligned} &y=\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )x+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{3} \end{aligned}

Hence, Degree = Highest power of the highest order derivative.

So, the degree of the above differential equation is 3.

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Gurleen Kaur

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