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

Question

Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=\sin^2\text{y}$

✓

Answer

We have

$\frac{\text{dy}}{\text{dx}}=\sin^2\text{y}$

$\Rightarrow\text{dx}=\frac{1}{\sin^2\text{y}}$

$\Rightarrow\text{dx}=\text{cosec}^2\text{y dy}$

Integrating both sides, we get

$\int\text{dx}=\text{cosec}^2\text{y dy}$

$\Rightarrow\text{x}=-\cot\text{y}+\text{C}$

$\Rightarrow\text{x}+\cot\text{y}=\text{C}$

Hence, $\Rightarrow\text{x}+\cot\text{y}=\text{C}$ is the required solution.

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

Evaluate the following integrals:
$\int\text{x}^3\cos\text{x}^4\text{dx}$

Give an example of a map:

Which is one-one but not onto.
Which is not one-one but onto.
Which is neither one-one nor onto.

Find which of the function:
$\begin{cases}\frac{1-\cos2\text{x}}{\text{x}^2},&\text{ if x}\neq0\\5,&\text{if x}=0\end{cases}$
at x = 0

$\text{If x}\sqrt{1+\text{y}}+\text{y}\sqrt{1+\text{x}}=0,$ for, < x < 1, prove that

For what value of k is the following function continuous at x = 2?
$\text{f(x)}=\begin{cases}2\text{x}+1,&\text{if }\text{ x}<2\\\text{k},&\text{x}=2\\3\text{x}-1,&\text{x}>2\end{cases}$

Evaluate the following definite integrals:
$\int_{0}^\limits{1}\text{x}(1-\text{x})^5\text{ dx}$

Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.

Find $\frac{\text{dy}}{\text{dx}}$ in the following cases:
$\tan^{-1}\big(\text{x}^2+\text{y}^2\big)=\text{a}$

If $\text{x}=\text{e}^{\frac{\text{x}}{\text{y}}},$ prove that $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}-\text{y}}{\text{x}\log\text{x}}.$

Two dice are thrown together. What is the probability that the sum of the numbers on the two dice is neither 9 nor 11?