Solve the following differential equation dy dx = 1- 2y 1+ 2y - Vidyadip

Question

Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=\frac{1-\cos2\text{y}}{1+\cos2\text{y}}$

✓

Answer

We have
$\frac{\text{dy}}{\text{dx}}=\frac{1-\cos2\text{y}}{1+\cos2\text{y}}$
$=\frac{2\sin^2\text{y}}{2\cos^2\text{y}}$
$\frac{\text{dy}}{\text{dx}}=\tan^2\text{y}$
$\frac{\text{dy}}{\tan^2\text{y}}=\text{dx}$
$\int\cot^2\text{y dy}=\int\text{dx}$
$\int(\text{cosec}^2\text{y}-1)\text{dy}=\int\text{dx}$
$-\cot\text{y}-\text{y}+\text{C}=\text{x}$
$\text{C}=\text{x}+\text{y}+\cot\text{y}$

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 "3 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

If $x ^{ x }+ y ^{ x }=1$, prove that $\frac{d y}{d x}=-\left\{\frac{x^x(1+\log x)+y^x \cdot \log y}{x \cdot y^{(x-1)}}\right\}$

State Rolle's theorem.

Find the shortest distance between the lines whose vector equations are $\vec r = \hat i + 2\hat j + 3\hat k$ + $\lambda \left( {\hat i - 3\hat j + 2\hat k} \right)$ and $\vec r = 4\hat i + 5\hat j + 6\hat k$ + $\mu \left( {2\hat i + 3\hat j + \hat k} \right)$

If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (-4, 3, -6) and (2, 9, 2) respectively, then find the angle between the lines AB and CD.

Write the minors and cofactors of element of the first column of the following matrices and hence evaluate the determinant in case:
$\text{A}=\begin{vmatrix}-1&4\\2&3 \end{vmatrix}$

Find the projection of $\overrightarrow{b} + \overrightarrow{c} $ on $\overrightarrow{a}$ where $\overrightarrow{a} = 2\hat{i} - 2\hat{j} + \hat{k}, \overrightarrow{b} = \hat{i} + 2\hat{j} - 2\hat{k} $ and $\overrightarrow{c} = 2\hat{i} - \hat{j} + 4\hat{k}.$

For each of the differential equations in find the general solution:
$\frac{\text{dy}}{\text{dx}}=\sqrt{4-\text{y}^2}(-2<\text{y}<2)$

Differentiate:$\tan(\text{x}^\circ+45^\circ)$

Find the mean and standard deviation of the following probability distributions:

$x_i$	$2$	$3$	$4$
$p_i$	$0.2$	$0.5$	$0.3$

Write a value of $\int\frac{\log\text{x}^{\text{n}}}{\text{x}}\text{ dx}$