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

If $\int\Big(\frac{\text{x}-1}{\text{x}^2}\Big)\text{e}^{\text{x}}\text{ dx}=\text{f(x)}\text{e}^{\text{x}}+\text{C},$ then write the value of f(x).

In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is $\frac{5}{6}.$ What is the probability that he will knock down fewer than 2 hurdles?

Prove that the function f given by f(x) = |x - 1|, x $\in$ R is not differentiable at x = 1.

Determine the value of $\lambda$ for which the following planes are perpendicular to other.
$2\text{x}-4\text{y}+3\text{z}=5$ and $\text{x}+2\text{y}+\lambda\text{z}=5$

If A, B and C are independent events such that P(A) = P(B) = P(C) = p, then find the probability of occurrence of at least two of A, B and C.

$\int\frac{2\text{x}}{(2\text{x}+1)^2}\text{dx}$

Evaluate the following integrals:

$\int\text{e}^{\text{x}}\sec\text{x}(1+\tan\text{x})\text{dx}$

Solve system of linear equations, using matrix method.

x - 2y - z = $\frac{3}{2}$

Write the plane $\vec{\text{r}}.(2\hat{\text{i}}+3\hat{\text{j}}-6\hat{\text{k}})=14$ in normal form.

If $y=\left(\sin ^{-1} x\right)^2$ then prove that $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}-2=0$.