Write the differential equation obtained by emliminating the abit… - Vidyadip

Question

Write the differential equation obtained by emliminating the abitrary constant C in the equation $\text{x}^{2}-\text{y}^{2}=\text{C}^{2}.$

✓

Answer

We have,
$\text{x}^{2}-\text{y}^{2}=\text{C}^{2}$
Differentiating with respect to x, we get
$2\text{x}-2\text{y}\frac{\text{dy}}{\text{dx}}=0$
$\Rightarrow 2\text{x}=2\text{y}\frac{\text{dy}}{\text{dx}}$
$\Rightarrow \text{x}\ \text{dx}=\text{y}\ \text{dy}$
$\Rightarrow \text{x}\ \text{dx}-\text{y}\ \text{dy}=0$
Hence, $ \text{x}\ \text{dx}-\text{y}\ \text{dy}=0$ is the differential equation.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "1 Marks Question" from Differential Equations→Differential Equations — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the relationship between a and b, so that the function f defined by f(x)= $ \left\{ \begin{array} { l } { a x + 1 , \text { if } x \leq 3 } \\ { b x + 3 , \text { if } x > 3 } \end{array} \right.$is continuous at x = 3.

Integrate the functions in Exercises:
$\frac{1}{\cos^2\text{x}(1-\tan\text{x})^2}$

Integrate the function x log 2x

If $A=\{1,2,3\}$ then find the number of all possible non-empty relations defined in A ?

Construct a $3 \times 4$ matrix $A = [a_{ij}]$ whose element $a_{ij}$ are given by: $a_{ij} = j$

If $A^T=$ $\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{and B}=\begin{bmatrix} -1 & 2 & 1 \\ 1 & 2 & 3 \\ \end{bmatrix},$ then find $A^T – B^T.$

A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

Write the value of the determinant $\begin{vmatrix} 2 & 3 & 4 \\ 5 & 6 & 8 \\ 6\text{x} & \text{9x} & 12\text{x} \end{vmatrix} $

Find derivative with respect to $x$ for $\cos (\sqrt{x})$.

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that at least one is a girl?