If y= show that d^2y dx^2 +2y dy dx =0 - Vidyadip

Question

If $\text{y}=\cot\text{x}$ show that $\frac{\text{d}^2\text{y}}{\text{dx}^2}+2\text{y}\frac{\text{dy}}{\text{dx}}=0$

✓

Answer

$\text{y}=\cot\text{x}$
Differentiating w.r.t.x
$\Rightarrow\frac{\text{dy}}{\text{dx}}=-\text{cosec}^2\text{x}$
Differentiating w.r.t.x
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}=-[2\text{cosec}\text{ x}(-\text{cosec}^2\times\cot\text{x})]=-2\frac{\text{dy}}{\text{dx}}.\text{y}$
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}+2\text{y}\frac{\text{dy}}{\text{dx}}=0$
Hence proved.

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 "2 Marks Questions" from Higher Order Derivatives→Higher Order Derivatives — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate $\begin{vmatrix}1&\text{x}&\text{y}\\1&\text{x}+\text{y}&\text{y}\\1&\text{x}&\text{x+y}\end{vmatrix}$

Evaluate the integral $\int_{0}^{\frac{\pi}{2}} \frac{\sin x}{1+\cos ^{2} x} d x$ using substitution.

Let $A = \{3, 5, 7\}, B = \{2, 6, 10\}$ and $R$ be a relation from $A$ to $B$ defined by $R = (x, y): x$ and $y$ are relatively prime. Then, write $R$ and $R^{-1}.$

Evaluate the definite integral in Exercise:
$\int\limits_{-1}^{1}\text{(x}+1)\ \text{dx}$

For what vaiue of $\lambda$ are the vectors $\vec{\text{a}}=2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$ perpendicular to each other?

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event the number is even, and B be the event the number is red. Are A and B independent?

To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:

₹ 50
₹ 20
₹ 40

The number of attempts made in three villages X, Y and Z are given below:

	(i)	(ii)	(iii)
X	400	300	100
Y	300	250	75
Z	500	400	150

Find the total cost incurred by the organisation for three villages separately, using matrices.

Find the value of $\sin \left[2 \sin ^{-1}(0.6)\right]$

If $\int\limits^{\text{a}}_03\text{x}^2\text{ dx}=8,$ Write the value of a.

The side of an equilataral triangle is inreasing at the rate of $\frac{1}{3}\text{cm}/\sec.$ Find the rate of increase of his primeter.