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  • The order and degree of the differential equation d^2y/dx^2+dy^1.4/4dx+x^1/2 = 0 respectively, are A. 2 and 4 B. 2 and 2 C. 2 and 3 D. 3 and 3

The order and degree of the differential equation \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{1 / 4}+x^{1 / 5}=0 respectively, are
A. 2 and 4
B. 2 and 2
C. 2 and 3
D. 3 and 3

 

Answers (1)

Solution

The differential equation is

\frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{1 / 4}+x^{1 / 5}=0

Order is defined as the number which represents the highest derivative in a differential equation.

\frac{d^{2} y}{d x^{2}}
Is the highest derivative in the given equation is second order hence the degree of the equation is 2 .
Integer powers on the differentials,
\\ \Rightarrow\left(\frac{d y}{d x}\right)^{\frac{1}{4}}=-\frac{d^{2} y}{d x^{2}}-x^{\frac{1}{5}} \\ \Rightarrow\left(\frac{d y}{d x}\right)^{\frac{1}{4}}=-\left(\frac{d^{2} y}{d x^{2}}+x^{\frac{1}{5}}\right)
Now for the degree to exit the differential equation must be a polynomial in some differentials.
Here differentials means
\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
Degree of differential equation is the highest integer power of the highest
order derivative in the equation.

Observe that
\left(\frac{d^{2} y}{d x^{2}}+x^{\frac{1}{5}}\right)^{4}
Of differential equation (a) the maximum power \mathrm{d}^{2} \mathrm{y} / \mathrm{d} \mathrm{x}^{2} \ will \ be \ 4
Highest order is \mathrm{d}^{2} \mathrm{y} / \mathrm{dx}^{2}and highest power is 4
Degree of the given differential equation is  4 .
Hence order is 2 and degree is 4

Option A is correct.

Posted by

infoexpert22

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