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  • The degree of the differential equation 1 + dy^2^3/2/dx is: A. 4 B. 3/4 C. not defined D. 2

The degree of the differential equation \left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=\frac{d^{2} y}{d x^{2}} is:
A. 4
B. 3/4
C. not defined
D. 2

 

Answers (1)

Generally, for a polynomial degree is the highest power.
$$ \left(1+\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}=\frac{d^{2} y}{d x^{2}} $$
Differential equation is Squaring both the sides,
$$ \Rightarrow\left(1+\left(\frac{d y}{d x}\right)^{2}\right)^{3}=\left(\frac{d^{2} y}{d x^{2}}\right)^{2} $$
Now for the degree to exit the differential equation must be a polynomial in
some differentials.
The given differential equation is polynomial in differential is

\frac{\mathrm{dy}}{\mathrm{dx}}$ and $\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}$
Degree of differential equation is the highest integer power of the highest order
derivative in the equation.
Highest derivative is
\frac{d^{2} y}{d x^{2}}$
There is only one term of the highest order derivative in the equation which is
\left(\frac{d^{2} y}{d x^{2}}\right)^{2}$  Whose power is 2 hence the degree is 2

Option D is correct.

Posted by

infoexpert22

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