Solve the following differential equations: 1+x^2 dy+ 1+y^2 dx=0 - Vidyadip

Question

Solve the following differential equations:
$\sqrt{1+\text{x}^2}\ \text{dy}+\sqrt{1+\text{y}^2}\ \text{dx}=0$

✓

Answer

$\sqrt{1+\text{x}^2}\ \text{dy}+\sqrt{1+\text{y}^2}\ \text{dx}=0$
$\sqrt{1+\text{x}^2}\ \text{dy}=-\sqrt{1+\text{y}^2}\ \text{dx}$
$\int\frac{\text{dy}}{\sqrt{1+\text{y}^2}}=-\int\frac{\text{dx}}{\sqrt{1+\text{x}^2}}$
$\log|\text{y}+\sqrt{1+\text{y}^2}|=-\log|\text{x}+\sqrt{1+\text{x}^2}|=\log|\text{c}|$
$(\text{y}+\sqrt{1+\text{y}^2})(\text{x}+\sqrt{1+\text{x}^2})=\text{c}$

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 Question" 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

The probability of a man hitting a target is 1/4. If he fires 7 times, what is the probability of his hitting the target at least twice?

Find the equation of the curve which passes through the origin and has the slope x + 3y − 1 at any point (x, y) on it.

Evaluate the following integrals:
$\int\Big(\frac{\text{x}+1}{\text{x}}\Big)(\text{x}+\log\text{x})^2\text{dx}$

Solve the following equation for x:
$\tan^{-1}2\text{x}+\tan^{-1}3\text{x}=\text{n}\pi+\frac{3\pi}{4}$

Find the slope of the normal at the point 't' on the curve $\text{x}=\frac{1}{\text{t}},\text{y}=\text{t}.$

Find the value of $\int \frac{x e^x}{(x+1)^2} d x$.

Discuss the continuity of the following functions at the indicated point:
$\text{f}\text{(x)}=\begin{cases}\text{|x|}\cos\Big(\frac{1}{\text{x}}\Big), & \text{ x}\neq 0\\0 &\text{ x} = 0\end{cases}\text{at x}=0$

If $\vec{\text{a}}=5\hat{\text{i}}-\hat{\text{j}}-3\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+3\hat{\text{j}}-5\hat{\text{k}},$ then show that the vectores $\vec{\text{a}}+\vec{\text{b}}$ and $\vec{\text{a}}-\vec{\text{b}}$ are orthonal.

Solve the following differential equation
$(\text{x}+2)\frac{\text{dy}}{\text{dx}}=\text{x}^2+3\text{x}+7$

Let $f: R \rightarrow R$ be the function defined by $f(x)=4 x-3$ for all $x \in R$. Then write $f^{-1}$.