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  • Family y = Ax + A3 of curves is represented by the differential equation of degree: A. 1 B. 2 C. 3 D. 4

Family y = Ax + A^3 of curves is represented by the differential equation of degree:
A. 1
B. 2
C. 3
D. 4

 

Answers (1)

y=A x+A^{3}$
let us find the differential equation representing it so we have to eliminate
the constant A
Differentiate with respect to x
$$ \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{A} $$
Put back value of A in y
\Rightarrow \mathrm{y}=\frac{\mathrm{dy}}{\mathrm{dx}} \mathrm{x}+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{3}$

Now for the degree to exit the differential equation must be a polynomial in some differentials.
Here the differentials mean
\frac{\mathrm{dy}}{\mathrm{dx}}$ or $\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}$ or $\ldots \frac{\mathrm{d}^{\mathrm{n}} \mathrm{y}}{\mathrm{dx}^{\mathrm{n}}}$
The given differential equation is polynomial in differentials
\frac{\mathrm{dy}}{\mathrm{dx}}$
Degree of differential equation is the highest integer power of the highest order derivative in the equation.
Highest derivative is
\frac{\mathrm{dy}}{\mathrm{dx}}$
And highest power to it is  3 .  Hence degree is 3 .

Option C is correct.

Posted by

infoexpert22

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