Solve the following differential equations: dy dx + =0 - Vidyadip

Question

Solve the following differential equations:

$\frac{\text{dy}}{\text{dx}}+\frac{\cos\text{x}\sin\text{y}}{\cos\text{y}}=0$

✓

Answer

$\frac{\text{dy}}{\text{dx}}+\frac{\cos\text{x}\sin\text{y}}{\cos\text{y}}=0$
$\frac{\text{dy}}{\text{dx}}=-\cos\text{x}\tan\text{y}$
$\frac{\text{dy}}{\tan\text{y}}=-\cos\text{x dx}$
$\int\cot\text{ y dy}=-\int\cos\text{x dx}$
$\log|\sin\text{y}|=-\sin\text{x + C}$
$\sin\text{x}+\log|\sin\text{y}|=\text{C}$

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" from DIFFERENTIAL EQUATIONS→DIFFERENTIAL EQUATIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

There are two bags I and II. Bag I contains 2 white and 3 red balls and Bag II contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag II.

If $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=8,$ find $\vec{\text{a}}.\vec{\text{b}}.$

Examine the following functions for continuity.
$\text f(\text X)=\frac{\text X^{2} - 25}{\text {X} + 5}$

Evaluate the following integrals:

$\int\text{e}^{\text{x}}\big(\cot\text{x}-\text{cosec}^2\text{x}\big)\text{dx}$

If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.

Find a solution of $ \left( x ^ { 3 } + x ^ { 2 } + x + 1 \right) \frac { d y } { d x } = 2 x ^ { 2 } + x$ which satisfy the condition y = 1 when x = 0.

Prove the following:
$2\tan^{-1}\frac{1}{2}+\tan^{-1}\frac{1}{7}=\tan^{-1}\frac{31}{17}$

Prove the following results:
$\tan^{-1}\frac{1}{4}+\tan^{-1}\frac{2}{9}=\sin^{-1}\frac{1}{\sqrt5}$

Using the fact that $\sin(\text{A}+\text{B})=\sin\text{A}\cos\text{B}+\cos\text{A}\sin\text{B}$and the differentiation, obtain the sum formula for cosines.

Using properties of determinants, prove the following:

$ \begin{vmatrix} a - b -c & 2a & 2a \\ 2b & b- c - a & 2b \\ 2c & 2c & c- a -b \end{vmatrix} = (a + b + c)^{3}$