Answer

Verified

414.6k+ views

**Hint:**We can find the degree of differential equation by using the formula-

Length of normal=$y\sqrt {1 + {{\left( {\dfrac{{dy}}{{dx}}} \right)}^2}} $ where y is the given function and $\dfrac{{dy}}{{dx}}$ is the derivative of the function.

**Complete step-by-step answer:**The degree is the power of the highest derivative .Here, we have to find the degree of differential equation of all curves having a normal of constant length c. We know that the if y=f(x) is any given function of a curve then at point $\left( {{{\text{x}}_1},{{\text{y}}_1}} \right)$ the length of normal is given as-

$ \Rightarrow $ Length of normal=$y\sqrt {1 + {{\left( {\dfrac{{dy}}{{dx}}} \right)}^2}} $ where y is the given function and $\dfrac{{dy}}{{dx}}$ is the derivative of the function

So on putting the value of normal length, we get-

$ \Rightarrow {\text{c = }}y\sqrt {1 + {{\left( {\dfrac{{dy}}{{dx}}} \right)}^2}} $ --- (i)

We have to find degree of this differential equation so first we will square both side to remove the square-root,

$ \Rightarrow {{\text{c}}^2} = {{\text{y}}^2}{\left( {1 + \dfrac{{dy}}{{dx}}} \right)^2}$

On simplifying and multiplying the function ${{\text{y}}^2}$ inside the bracket, we get-

$

\Rightarrow {{\text{c}}^2} = {{\text{y}}^2}\left( {1 + {{\left( {\dfrac{{dy}}{{dx}}} \right)}^2} + 2\dfrac{{dy}}{{dx}}} \right) \\

\Rightarrow {{\text{c}}^2} = {{\text{y}}^2} + {{\text{y}}^2}{\left( {\dfrac{{dy}}{{dx}}} \right)^2} + 2{{\text{y}}^2}\dfrac{{dy}}{{dx}} \\

$

Here the highest derivative is ${\left( {\dfrac{{dy}}{{dx}}} \right)^2}$ and its power is $2$ so the degree of the differential equation is also $2$

**Hence the answer is ‘D’.**

**Note:**Here the student may go wrong if they try to find the degree of differential equation in eq. (i) as the derivative is also under the square-root. So first we have to solve the eq. (i) and remove the square-root, only then can we easily find the degree.

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Name 10 Living and Non living things class 9 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE